LMFDB - Embedded newform 950.2.u.f.99.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(99,950)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 2]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("950.99");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.u (of order $18$, degree $6$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 190)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			99.4
Character	$\chi$	$=$	950.99
Dual form			950.2.u.f.499.4

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.342020 - 0.939693i) q^{2} +(2.25357 - 0.397366i) q^{3} +(-0.766044 - 0.642788i) q^{4} +(0.397366 - 2.25357i) q^{6} +(-2.39766 - 1.38429i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(2.10161 - 0.764925i) q^{9} +O(q^{10})$	\(q+(0.342020 - 0.939693i) q^{2} +(2.25357 - 0.397366i) q^{3} +(-0.766044 - 0.642788i) q^{4} +(0.397366 - 2.25357i) q^{6} +(-2.39766 - 1.38429i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(2.10161 - 0.764925i) q^{9} +(-1.21064 - 2.09689i) q^{11} +(-1.98176 - 1.14417i) q^{12} +(1.70381 + 0.300428i) q^{13} +(-2.12086 + 1.77961i) q^{14} +(0.173648 + 0.984808i) q^{16} +(1.38022 - 3.79213i) q^{17} -2.23649i q^{18} +(-0.0664727 - 4.35839i) q^{19} +(-5.95337 - 2.16685i) q^{21} +(-2.38450 + 0.420451i) q^{22} +(5.74414 - 6.84561i) q^{23} +(-1.75297 + 1.47092i) q^{24} +(0.865049 - 1.49831i) q^{26} +(-1.51309 + 0.873583i) q^{27} +(0.946910 + 2.60161i) q^{28} +(-4.18479 + 1.52314i) q^{29} +(0.953372 - 1.65129i) q^{31} +(0.984808 + 0.173648i) q^{32} +(-3.56150 - 4.24443i) q^{33} +(-3.09138 - 2.59397i) q^{34} +(-2.10161 - 0.764925i) q^{36} +2.89348i q^{37} +(-4.11828 - 1.42819i) q^{38} +3.95905 q^{39} +(-0.808735 - 4.58656i) q^{41} +(-4.07235 + 4.85323i) q^{42} +(1.91317 + 2.28003i) q^{43} +(-0.420451 + 2.38450i) q^{44} +(-4.46815 - 7.73907i) q^{46} +(3.39608 + 9.33064i) q^{47} +(0.782658 + 2.15033i) q^{48} +(0.332517 + 0.575937i) q^{49} +(1.60357 - 9.09430i) q^{51} +(-1.11209 - 1.32533i) q^{52} +(-7.18700 + 8.56514i) q^{53} +(0.303392 + 1.72062i) q^{54} +2.76858 q^{56} +(-1.88168 - 9.79554i) q^{57} +4.45336i q^{58} +(1.89474 + 0.689630i) q^{59} +(6.66844 + 5.59549i) q^{61} +(-1.22563 - 1.46065i) q^{62} +(-6.09783 - 1.07521i) q^{63} +(0.500000 - 0.866025i) q^{64} +(-5.20657 + 1.89504i) q^{66} +(4.61495 + 12.6795i) q^{67} +(-3.49485 + 2.01775i) q^{68} +(10.2246 - 17.7096i) q^{69} +(10.2246 - 8.57949i) q^{71} +(-1.43759 + 1.71325i) q^{72} +(5.62193 - 0.991298i) q^{73} +(2.71898 + 0.989627i) q^{74} +(-2.75060 + 3.38145i) q^{76} +6.70352i q^{77} +(1.35407 - 3.72029i) q^{78} +(-1.16772 - 6.62249i) q^{79} +(-8.20248 + 6.88270i) q^{81} +(-4.58656 - 0.808735i) q^{82} +(14.6821 + 8.47670i) q^{83} +(3.16772 + 5.48666i) q^{84} +(2.79687 - 1.01798i) q^{86} +(-8.82549 + 5.09540i) q^{87} +(2.09689 + 1.21064i) q^{88} +(-0.964193 + 5.46821i) q^{89} +(-3.66929 - 3.07890i) q^{91} +(-8.80054 + 1.55177i) q^{92} +(1.49233 - 4.10014i) q^{93} +9.92946 q^{94} +2.28834 q^{96} +(2.63009 - 7.22610i) q^{97} +(0.654931 - 0.115482i) q^{98} +(-4.14827 - 3.48081i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 6 q^{6} - 18 q^{9}+O(q^{10}) $ 24 * q + 6 * q^6 - 18 * q^9	$ 24 q + 6 q^{6} - 18 q^{9} - 12 q^{11} + 12 q^{14} - 12 q^{19} - 72 q^{21} - 6 q^{24} - 6 q^{26} - 72 q^{29} - 48 q^{31} + 12 q^{34} + 18 q^{36} + 24 q^{39} - 24 q^{41} + 18 q^{44} - 36 q^{46} - 54 q^{51} - 18 q^{54} + 24 q^{56} + 54 q^{59} + 108 q^{61} + 12 q^{64} - 78 q^{66} + 48 q^{69} + 48 q^{71} - 30 q^{74} + 18 q^{76} + 72 q^{79} - 18 q^{81} - 24 q^{84} + 48 q^{86} - 36 q^{89} + 24 q^{91} - 36 q^{94} - 36 q^{99}+O(q^{100}) $ 24 * q + 6 * q^6 - 18 * q^9 - 12 * q^11 + 12 * q^14 - 12 * q^19 - 72 * q^21 - 6 * q^24 - 6 * q^26 - 72 * q^29 - 48 * q^31 + 12 * q^34 + 18 * q^36 + 24 * q^39 - 24 * q^41 + 18 * q^44 - 36 * q^46 - 54 * q^51 - 18 * q^54 + 24 * q^56 + 54 * q^59 + 108 * q^61 + 12 * q^64 - 78 * q^66 + 48 * q^69 + 48 * q^71 - 30 * q^74 + 18 * q^76 + 72 * q^79 - 18 * q^81 - 24 * q^84 + 48 * q^86 - 36 * q^89 + 24 * q^91 - 36 * q^94 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$-1$	$e\left(\frac{1}{9}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.342020	−	0.939693i	0.241845	−	0.664463i
$2$	0.342020	−	0.939693i	0.241845	−	0.664463i
$3$	2.25357	−	0.397366i	1.30110	−	0.229419i	0.520184	−	0.854054i	$-0.325863\pi$
$3$	2.25357	−	0.397366i	1.30110	−	0.229419i	0.780917	+	0.624635i	$0.214752\pi$
$4$	−0.766044	−	0.642788i	−0.383022	−	0.321394i
$5$		0			0
$5$		0			0
$6$	0.397366	−	2.25357i	0.162224	−	0.920017i
$7$	−2.39766	−	1.38429i	−0.906230	−	0.523212i	−0.0270141	−	0.999635i	$-0.508600\pi$
$7$	−2.39766	−	1.38429i	−0.906230	−	0.523212i	−0.879216	+	0.476423i	$0.841933\pi$
$8$	−0.866025	+	0.500000i	−0.306186	+	0.176777i
$9$	2.10161	−	0.764925i	0.700538	−	0.254975i
$10$		0			0
$11$	−1.21064	−	2.09689i	−0.365022	−	0.632237i	0.623758	−	0.781618i	$-0.285605\pi$
$11$	−1.21064	−	2.09689i	−0.365022	−	0.632237i	−0.988780	+	0.149381i	$0.952272\pi$
$12$	−1.98176	−	1.14417i	−0.572085	−	0.330293i
$13$	1.70381	+	0.300428i	0.472553	+	0.0833238i	0.404853	−	0.914382i	$-0.367323\pi$
$13$	1.70381	+	0.300428i	0.472553	+	0.0833238i	0.0677001	+	0.997706i	$0.478434\pi$
$14$	−2.12086	+	1.77961i	−0.566822	+	0.475620i
$15$		0			0
$16$	0.173648	+	0.984808i	0.0434120	+	0.246202i
$17$	1.38022	−	3.79213i	0.334753	−	0.919728i	−0.652103	−	0.758130i	$-0.726113\pi$
$17$	1.38022	−	3.79213i	0.334753	−	0.919728i	0.986857	−	0.161597i	$-0.0516646\pi$
$18$		−	2.23649i		−	0.527146i
$19$	−0.0664727	−	4.35839i	−0.0152499	−	0.999884i
$19$	−0.0664727	−	4.35839i	−0.0152499	−	0.999884i
$20$		0			0
$21$	−5.95337	−	2.16685i	−1.29913	−	0.472846i
$22$	−2.38450	+	0.420451i	−0.508377	+	0.0896406i
$23$	5.74414	−	6.84561i	1.19774	−	1.42741i	0.320568	−	0.947225i	$-0.396126\pi$
$23$	5.74414	−	6.84561i	1.19774	−	1.42741i	0.877169	−	0.480182i	$-0.159429\pi$
$24$	−1.75297	+	1.47092i	−0.357823	+	0.300249i
$25$		0			0
$26$	0.865049	−	1.49831i	0.169650	−	0.293842i
$27$	−1.51309	+	0.873583i	−0.291194	+	0.168121i
$28$	0.946910	+	2.60161i	0.178949	+	0.491659i
$29$	−4.18479	+	1.52314i	−0.777096	+	0.282840i	−0.699961	−	0.714181i	$-0.746799\pi$
$29$	−4.18479	+	1.52314i	−0.777096	+	0.282840i	−0.0771351	+	0.997021i	$0.524577\pi$
$30$		0			0
$31$	0.953372	−	1.65129i	0.171231	−	0.296580i	−0.767620	−	0.640906i	$-0.778559\pi$
$31$	0.953372	−	1.65129i	0.171231	−	0.296580i	0.938850	+	0.344325i	$0.111892\pi$
$32$	0.984808	+	0.173648i	0.174091	+	0.0306970i
$33$	−3.56150	−	4.24443i	−0.619978	−	0.738861i
$34$	−3.09138	−	2.59397i	−0.530167	−	0.444863i
$35$		0			0
$36$	−2.10161	−	0.764925i	−0.350269	−	0.127487i
$37$			2.89348i			0.475685i	0.971304	+	0.237842i	$0.0764402\pi$
$37$			2.89348i			0.475685i	−0.971304	+	0.237842i	$0.923560\pi$
$38$	−4.11828	−	1.42819i	−0.668074	−	0.231684i
$39$	3.95905			0.633955
$40$		0			0
$41$	−0.808735	−	4.58656i	−0.126303	−	0.716301i	−0.980525	−	0.196393i	$-0.937077\pi$
$41$	−0.808735	−	4.58656i	−0.126303	−	0.716301i	0.854222	−	0.519908i	$-0.174034\pi$
$42$	−4.07235	+	4.85323i	−0.628377	+	0.748870i
$43$	1.91317	+	2.28003i	0.291756	+	0.347702i	0.891934	−	0.452165i	$-0.149348\pi$
$43$	1.91317	+	2.28003i	0.291756	+	0.347702i	−0.600178	+	0.799866i	$0.704904\pi$
$44$	−0.420451	+	2.38450i	−0.0633854	+	0.359477i
$45$		0			0
$46$	−4.46815	−	7.73907i	−0.658793	−	1.14106i
$47$	3.39608	+	9.33064i	0.495369	+	1.36101i	0.895706	+	0.444646i	$0.146671\pi$
$47$	3.39608	+	9.33064i	0.495369	+	1.36101i	−0.400338	+	0.916368i	$0.631107\pi$
$48$	0.782658	+	2.15033i	0.112967	+	0.310374i
$49$	0.332517	+	0.575937i	0.0475025	+	0.0822767i
$50$		0			0
$51$	1.60357	−	9.09430i	0.224545	−	1.27346i
$52$	−1.11209	−	1.32533i	−0.154218	−	0.183790i
$53$	−7.18700	+	8.56514i	−0.987211	+	1.17651i	−0.00291297	+	0.999996i	$0.500927\pi$
$53$	−7.18700	+	8.56514i	−0.987211	+	1.17651i	−0.984298	+	0.176516i	$0.943517\pi$
$54$	0.303392	+	1.72062i	0.0412865	+	0.234147i
$55$		0			0
$56$	2.76858			0.369967
$57$	−1.88168	−	9.79554i	−0.249234	−	1.29745i
$58$			4.45336i			0.584755i
$59$	1.89474	+	0.689630i	0.246674	+	0.0897821i	0.462399	−	0.886672i	$-0.346989\pi$
$59$	1.89474	+	0.689630i	0.246674	+	0.0897821i	−0.215724	+	0.976454i	$0.569211\pi$
$60$		0			0
$61$	6.66844	+	5.59549i	0.853806	+	0.716429i	0.960624	−	0.277850i	$-0.0896218\pi$
$61$	6.66844	+	5.59549i	0.853806	+	0.716429i	−0.106818	+	0.994279i	$0.534066\pi$
$62$	−1.22563	−	1.46065i	−0.155655	−	0.185503i
$63$	−6.09783	−	1.07521i	−0.768255	−	0.135464i
$64$	0.500000	−	0.866025i	0.0625000	−	0.108253i
$65$		0			0
$66$	−5.20657	+	1.89504i	−0.640884	+	0.233263i
$67$	4.61495	+	12.6795i	0.563805	+	1.54904i	0.814011	+	0.580850i	$0.197280\pi$
$67$	4.61495	+	12.6795i	0.563805	+	1.54904i	−0.250205	+	0.968193i	$0.580498\pi$
$68$	−3.49485	+	2.01775i	−0.423813	+	0.244688i
$69$	10.2246	−	17.7096i	1.23090	−	2.13199i
$70$		0			0
$71$	10.2246	−	8.57949i	1.21344	−	1.01820i	0.214300	−	0.976768i	$-0.431253\pi$
$71$	10.2246	−	8.57949i	1.21344	−	1.01820i	0.999141	−	0.0414306i	$-0.0131916\pi$
$72$	−1.43759	+	1.71325i	−0.169421	+	0.201909i
$73$	5.62193	−	0.991298i	0.657997	−	0.116023i	0.165327	−	0.986239i	$-0.447132\pi$
$73$	5.62193	−	0.991298i	0.657997	−	0.116023i	0.492670	+	0.870216i	$0.336021\pi$
$74$	2.71898	+	0.989627i	0.316075	+	0.115042i
$75$		0			0
$76$	−2.75060	+	3.38145i	−0.315515	+	0.387879i
$77$			6.70352i			0.763937i
$78$	1.35407	−	3.72029i	0.153319	−	0.421240i
$79$	−1.16772	−	6.62249i	−0.131379	−	0.745088i	−0.977313	−	0.211800i	$-0.932067\pi$
$79$	−1.16772	−	6.62249i	−0.131379	−	0.745088i	0.845934	−	0.533288i	$-0.179044\pi$
$80$		0			0
$81$	−8.20248	+	6.88270i	−0.911387	+	0.764744i
$82$	−4.58656	−	0.808735i	−0.506501	−	0.0893098i
$83$	14.6821	+	8.47670i	1.61157	+	0.930439i	0.989007	+	0.147866i	$0.0472404\pi$
$83$	14.6821	+	8.47670i	1.61157	+	0.930439i	0.622559	+	0.782573i	$0.286093\pi$
$84$	3.16772	+	5.48666i	0.345627	+	0.598643i
$85$		0			0
$86$	2.79687	−	1.01798i	0.301595	−	0.109771i
$87$	−8.82549	+	5.09540i	−0.946192	+	0.546284i
$88$	2.09689	+	1.21064i	0.223530	+	0.129055i
$89$	−0.964193	+	5.46821i	−0.102204	+	0.579629i	0.890096	+	0.455773i	$0.150637\pi$
$89$	−0.964193	+	5.46821i	−0.102204	+	0.579629i	−0.992300	+	0.123856i	$0.960474\pi$
$90$		0			0
$91$	−3.66929	−	3.07890i	−0.384646	−	0.322756i
$92$	−8.80054	+	1.55177i	−0.917520	+	0.161783i
$93$	1.49233	−	4.10014i	0.154747	−	0.425165i
$94$	9.92946			1.02415
$95$		0			0
$96$	2.28834			0.233553
$97$	2.63009	−	7.22610i	0.267045	−	0.733699i	−0.731604	−	0.681730i	$-0.761228\pi$
$97$	2.63009	−	7.22610i	0.267045	−	0.733699i	0.998649	−	0.0519694i	$-0.0165498\pi$
$98$	0.654931	−	0.115482i	0.0661580	−	0.0116654i
$99$	−4.14827	−	3.48081i	−0.416917	−	0.349835i
$100$		0			0
$101$	−1.82471	+	10.3484i	−0.181565	+	1.02971i	0.748724	+	0.662882i	$0.230667\pi$
$101$	−1.82471	+	10.3484i	−0.181565	+	1.02971i	−0.930289	+	0.366826i	$0.880444\pi$
$102$	−7.99740	−	4.61730i	−0.791860	−	0.457181i
$103$	−8.92940	+	5.15539i	−0.879840	+	0.507976i	−0.870606	−	0.491982i	$-0.836273\pi$
$103$	−8.92940	+	5.15539i	−0.879840	+	0.507976i	−0.00923425	+	0.999957i	$0.502939\pi$
$104$	−1.62576	+	0.591728i	−0.159419	+	0.0580237i
$105$		0			0
$106$	5.59050	+	9.68302i	0.542997	+	0.940498i
$107$	−6.09138	−	3.51686i	−0.588876	−	0.339987i	0.175777	−	0.984430i	$-0.443756\pi$
$107$	−6.09138	−	3.51686i	−0.588876	−	0.339987i	−0.764653	+	0.644442i	$0.777090\pi$
$108$	1.72062	+	0.303392i	0.165567	+	0.0291939i
$109$	−4.78492	+	4.01503i	−0.458312	+	0.384570i	−0.842510	−	0.538681i	$-0.818923\pi$
$109$	−4.78492	+	4.01503i	−0.458312	+	0.384570i	0.384197	+	0.923251i	$0.374478\pi$
$110$		0			0
$111$	1.14977	+	6.52066i	0.109131	+	0.618914i
$112$	0.946910	−	2.60161i	0.0894746	−	0.245829i
$113$			7.50521i			0.706031i	0.935618	+	0.353015i	$0.114844\pi$
$113$			7.50521i			0.706031i	−0.935618	+	0.353015i	$0.885156\pi$
$114$	−9.84837	−	1.58207i	−0.922384	−	0.148175i
$115$		0			0
$116$	4.18479	+	1.52314i	0.388548	+	0.141420i
$117$	3.81056	−	0.671905i	0.352287	−	0.0621177i
$118$	1.29608	−	1.54461i	0.119314	−	0.142193i
$119$	−8.55872	+	7.18162i	−0.784577	+	0.658338i
$120$		0			0
$121$	2.56869	−	4.44911i	0.233518	−	0.404464i
$122$	7.53878	−	4.35252i	0.682529	−	0.394058i
$123$	−3.64509	−	10.0148i	−0.328666	−	0.903003i
$124$	−1.79175	+	0.652145i	−0.160904	+	0.0585644i
$125$		0			0
$126$	−3.09595	+	5.36235i	−0.275809	+	0.477716i
$127$	12.8097	+	2.25870i	1.13668	+	0.200427i	0.710152	−	0.704049i	$-0.248626\pi$
$127$	12.8097	+	2.25870i	1.13668	+	0.200427i	0.426526	+	0.904476i	$0.359737\pi$
$128$	−0.642788	−	0.766044i	−0.0568149	−	0.0677094i
$129$	5.21748	+	4.37799i	0.459374	+	0.385460i
$130$		0			0
$131$	−4.41978	−	1.60867i	−0.386158	−	0.140550i	0.141643	−	0.989918i	$-0.454761\pi$
$131$	−4.41978	−	1.60867i	−0.386158	−	0.140550i	−0.527802	+	0.849368i	$0.676984\pi$
$132$			5.54072i			0.482257i
$133$	−5.87390	+	10.5420i	−0.509332	+	0.914104i
$134$	13.4932			1.16564
$135$		0			0
$136$	0.700758	+	3.97420i	0.0600895	+	0.340785i
$137$	14.1629	−	16.8787i	1.21002	−	1.44204i	0.346258	−	0.938139i	$-0.387452\pi$
$137$	14.1629	−	16.8787i	1.21002	−	1.44204i	0.863760	−	0.503903i	$-0.168103\pi$
$138$	−13.1445	−	15.6651i	−1.11894	−	1.33350i
$139$	2.26902	−	12.8682i	0.192456	−	1.09147i	−0.723540	−	0.690282i	$-0.757486\pi$
$139$	2.26902	−	12.8682i	0.192456	−	1.09147i	0.915996	−	0.401188i	$-0.131403\pi$
$140$		0			0
$141$	11.3610	+	19.6778i	0.956767	+	1.65717i
$142$	−4.56505	−	12.5424i	−0.383091	−	1.05253i
$143$	−1.43274	−	3.93643i	−0.119812	−	0.329180i
$144$	1.11825	+	1.93686i	0.0931871	+	0.161405i
$145$		0			0
$146$	0.991298	−	5.62193i	0.0820404	−	0.465274i
$147$	0.978209	+	1.16578i	0.0806813	+	0.0961523i
$148$	1.85989	−	2.21653i	0.152882	−	0.182198i
$149$	−0.359724	−	2.04010i	−0.0294697	−	0.167131i	0.966521	−	0.256587i	$-0.0825982\pi$
$149$	−0.359724	−	2.04010i	−0.0294697	−	0.167131i	−0.995991	+	0.0894563i	$0.971487\pi$
$150$		0			0
$151$	−3.55532			−0.289328			−0.144664	−	0.989481i	$-0.546210\pi$
$151$	−3.55532			−0.289328			−0.144664	+	0.989481i	$0.546210\pi$
$152$	2.23676	+	3.74124i	0.181425	+	0.303455i
$153$		−	9.02537i		−	0.729658i
$154$	6.29925	+	2.29274i	0.507608	+	0.184754i
$155$		0			0
$156$	−3.03281	−	2.54483i	−0.242819	−	0.203749i
$157$	5.92056	+	7.05585i	0.472512	+	0.563118i	0.948681	−	0.316236i	$-0.102419\pi$
$157$	5.92056	+	7.05585i	0.472512	+	0.563118i	−0.476168	+	0.879354i	$0.657975\pi$
$158$	−6.62249	−	1.16772i	−0.526857	−	0.0928991i
$159$	−12.7929	+	22.1580i	−1.01455	+	1.75725i
$160$		0			0
$161$	−23.2488	+	8.46188i	−1.83226	+	0.666889i
$162$	3.66221	+	10.0618i	0.287730	+	0.790532i
$163$	−17.5880	+	10.1545i	−1.37760	+	0.795359i	−0.991870	−	0.127253i	$-0.959384\pi$
$163$	−17.5880	+	10.1545i	−1.37760	+	0.795359i	−0.385731	+	0.922611i	$0.626051\pi$
$164$	−2.32866	+	4.03336i	−0.181838	+	0.314952i
$165$		0			0
$166$	12.9871	−	10.8974i	1.00799	−	0.845805i
$167$	7.00352	−	8.34647i	0.541949	−	0.645869i	−0.423675	−	0.905814i	$-0.639260\pi$
$167$	7.00352	−	8.34647i	0.541949	−	0.645869i	0.965623	+	0.259945i	$0.0837045\pi$
$168$	6.23920	−	1.10014i	0.481364	−	0.0848775i
$169$	−9.40328	−	3.42251i	−0.723329	−	0.263270i
$170$		0			0
$171$	−3.47354	−	9.10881i	−0.265628	−	0.696568i
$172$		−	2.97637i		−	0.226946i
$173$	5.71759	−	15.7089i	0.434700	−	1.19433i	−0.508196	−	0.861242i	$-0.669687\pi$
$173$	5.71759	−	15.7089i	0.434700	−	1.19433i	0.942896	−	0.333087i	$-0.108090\pi$
$174$	1.76961	+	10.0360i	0.134154	+	0.760826i
$175$		0			0
$176$	1.85481	−	1.55637i	0.139812	−	0.117316i
$177$	4.54397	+	0.801225i	0.341546	+	0.0602238i
$178$	4.80866	+	2.77628i	0.360424	+	0.208091i
$179$	−12.7705	−	22.1191i	−0.954510	−	1.65326i	−0.735486	−	0.677540i	$-0.763046\pi$
$179$	−12.7705	−	22.1191i	−0.954510	−	1.65326i	−0.219024	−	0.975719i	$-0.570287\pi$
$180$		0			0
$181$	−1.96483	+	0.715139i	−0.146044	+	0.0531558i	−0.414008	−	0.910273i	$-0.635872\pi$
$181$	−1.96483	+	0.715139i	−0.146044	+	0.0531558i	0.267964	+	0.963429i	$0.413649\pi$
$182$	−4.14819	+	2.39496i	−0.307484	+	0.177526i
$183$	17.2513	+	9.96003i	1.27525	+	0.736266i
$184$	−1.55177	+	8.80054i	−0.114398	+	0.648784i
$185$		0			0
$186$	−3.34246	−	2.80466i	−0.245081	−	0.205648i
$187$	−9.62266	+	1.69673i	−0.703678	+	0.124077i
$188$	3.39608	−	9.33064i	0.247684	−	0.680507i
$189$	4.83717			0.351852
$190$		0			0
$191$	12.9071			0.933924			0.466962	−	0.884278i	$-0.345349\pi$
$191$	12.9071			0.933924			0.466962	+	0.884278i	$0.345349\pi$
$192$	0.782658	−	2.15033i	0.0564835	−	0.155187i
$193$	−21.1670	+	3.73231i	−1.52363	+	0.268657i	−0.871859	−	0.489757i	$-0.837085\pi$
$193$	−21.1670	+	3.73231i	−1.52363	+	0.268657i	−0.651772	+	0.758415i	$0.725974\pi$
$194$	−5.89077	−	4.94294i	−0.422933	−	0.354883i
$195$		0			0
$196$	0.115482	−	0.654931i	0.00824871	−	0.0467808i
$197$	9.82570	+	5.67287i	0.700052	+	0.404175i	0.807367	−	0.590050i	$-0.200892\pi$
$197$	9.82570	+	5.67287i	0.700052	+	0.404175i	−0.107315	+	0.994225i	$0.534225\pi$
$198$	−4.68968	+	2.70759i	−0.333281	+	0.192420i
$199$	−12.7763	+	4.65019i	−0.905688	+	0.329643i	−0.752530	−	0.658558i	$-0.771167\pi$
$199$	−12.7763	+	4.65019i	−0.905688	+	0.329643i	−0.153158	+	0.988202i	$0.548944\pi$
$200$		0			0
$201$	15.4385	+	26.7403i	1.08895	+	1.88611i
$202$	9.10027	+	5.25404i	0.640292	+	0.369673i
$203$	12.1422	+	2.14099i	0.852214	+	0.150268i
$204$	−7.07411	+	5.93589i	−0.495287	+	0.415595i
$205$		0			0
$206$	1.79045	+	10.1541i	0.124746	+	0.707472i
$207$	6.83560	−	18.7807i	0.475107	−	1.30535i
$208$			1.73010i			0.119961i
$209$	−9.05861	+	5.41584i	−0.626597	+	0.374621i
$210$		0			0
$211$	−4.18459	−	1.52307i	−0.288079	−	0.104852i	0.193939	−	0.981014i	$-0.437874\pi$
$211$	−4.18459	−	1.52307i	−0.288079	−	0.104852i	−0.482018	+	0.876161i	$0.660096\pi$
$212$	11.0111	−	1.94156i	0.756247	−	0.133347i
$213$	19.6328	−	23.3974i	1.34522	−	1.60317i
$214$	−5.38814	+	4.52119i	−0.368326	+	0.309062i
$215$		0			0
$216$	0.873583	−	1.51309i	0.0594398	−	0.102953i
$217$	−4.57173	+	2.63949i	−0.310349	+	0.179180i
$218$	2.13635	+	5.86958i	0.144692	+	0.397538i
$219$	12.2755	−	4.46792i	0.829503	−	0.301914i
$220$		0			0
$221$	3.49091	−	6.04643i	0.234824	−	0.406727i
$222$	6.52066	+	1.14977i	0.437638	+	0.0771674i
$223$	12.7480	+	15.1924i	0.853667	+	1.01736i	0.999606	+	0.0280676i	$0.00893537\pi$
$223$	12.7480	+	15.1924i	0.853667	+	1.01736i	−0.145939	+	0.989294i	$0.546620\pi$
$224$	−2.12086	−	1.77961i	−0.141706	−	0.118905i
$225$		0			0
$226$	7.05259	+	2.56693i	0.469131	+	0.170750i
$227$		−	12.8345i		−	0.851857i	−0.904757	−	0.425928i	$-0.859948\pi$
$227$		−	12.8345i		−	0.851857i	0.904757	−	0.425928i	$-0.140052\pi$
$228$	−4.85500	+	8.71334i	−0.321531	+	0.577055i
$229$	11.4892			0.759230			0.379615	−	0.925145i	$-0.376056\pi$
$229$	11.4892			0.759230			0.379615	+	0.925145i	$0.376056\pi$
$230$		0			0
$231$	2.66375	+	15.1069i	0.175262	+	0.993959i
$232$	2.86257	−	3.41147i	0.187937	−	0.223974i
$233$	1.75412	+	2.09048i	0.114916	+	0.136952i	0.820436	−	0.571738i	$-0.193731\pi$
$233$	1.75412	+	2.09048i	0.114916	+	0.136952i	−0.705520	+	0.708690i	$0.749286\pi$
$234$	0.671905	−	3.81056i	0.0439238	−	0.249104i
$235$		0			0
$236$	−1.00817	−	1.74620i	−0.0656264	−	0.113668i
$237$	−5.26310	−	14.4602i	−0.341875	−	0.939294i
$238$	3.82126	+	10.4988i	0.247696	+	0.680538i
$239$	12.5128	+	21.6728i	0.809386	+	1.40190i	0.913290	+	0.407310i	$0.133533\pi$
$239$	12.5128	+	21.6728i	0.809386	+	1.40190i	−0.103904	+	0.994587i	$0.533133\pi$
$240$		0			0
$241$	4.37954	−	24.8376i	0.282111	−	1.59993i	−0.433316	−	0.901242i	$-0.642656\pi$
$241$	4.37954	−	24.8376i	0.282111	−	1.59993i	0.715426	−	0.698688i	$-0.246232\pi$
$242$	−3.30225	−	3.93547i	−0.212277	−	0.252981i
$243$	−12.3808	+	14.7548i	−0.794227	+	0.946523i
$244$	−1.51161	−	8.57278i	−0.0967711	−	0.548816i
$245$		0			0
$246$	−10.6575			−0.679499
$247$	1.19613	−	7.44586i	0.0761077	−	0.473769i
$248$			1.90674i			0.121078i
$249$	36.4555	+	13.2687i	2.31027	+	0.840870i
$250$		0			0
$251$	−2.55784	−	2.14629i	−0.161450	−	0.135472i	0.558484	−	0.829515i	$-0.311383\pi$
$251$	−2.55784	−	2.14629i	−0.161450	−	0.135472i	−0.719933	+	0.694043i	$0.755828\pi$
$252$	3.98008	+	4.74327i	0.250721	+	0.298798i
$253$	−21.3086	−	3.75728i	−1.33966	−	0.236218i
$254$	6.50366	−	11.2647i	0.408076	−	0.706808i
$255$		0			0
$256$	−0.939693	+	0.342020i	−0.0587308	+	0.0213763i
$257$	3.24404	+	8.91294i	0.202358	+	0.555974i	0.998812	−	0.0487248i	$-0.0155157\pi$
$257$	3.24404	+	8.91294i	0.202358	+	0.555974i	−0.796454	+	0.604699i	$0.793294\pi$
$258$	5.89845	−	3.40547i	0.367221	−	0.212015i
$259$	4.00541	−	6.93758i	0.248884	−	0.431080i
$260$		0			0
$261$	−7.62973	+	6.40210i	−0.472268	+	0.396280i
$262$	−3.02331	+	3.60304i	−0.186781	+	0.222597i
$263$	27.8496	−	4.91064i	1.71728	−	0.302803i	0.773603	−	0.633671i	$-0.218453\pi$
$263$	27.8496	−	4.91064i	1.71728	−	0.302803i	0.943677	+	0.330868i	$0.107341\pi$
$264$	5.20657	+	1.89504i	0.320442	+	0.116631i
$265$		0			0
$266$	7.89721	+	9.12522i	0.484209	+	0.559503i
$267$			12.7061i			0.777603i
$268$	4.61495	−	12.6795i	0.281903	−	0.774521i
$269$	0.907359	+	5.14589i	0.0553227	+	0.313750i	0.999894	−	0.0145556i	$-0.00463336\pi$
$269$	0.907359	+	5.14589i	0.0553227	+	0.313750i	−0.944571	+	0.328306i	$0.893522\pi$
$270$		0			0
$271$	0.277215	−	0.232611i	0.0168396	−	0.0141301i	−0.634329	−	0.773063i	$-0.718724\pi$
$271$	0.277215	−	0.232611i	0.0168396	−	0.0141301i	0.651169	+	0.758933i	$0.274279\pi$
$272$	3.97420	+	0.700758i	0.240971	+	0.0424897i
$273$	−9.49245	−	5.48047i	−0.574509	−	0.331693i
$274$	−11.0168	−	19.0816i	−0.665548	−	1.15276i
$275$		0			0
$276$	−19.2160	+	6.99407i	−1.15667	+	0.420993i
$277$	−11.3195	+	6.53530i	−0.680121	+	0.392668i	−0.799901	−	0.600132i	$-0.795115\pi$
$277$	−11.3195	+	6.53530i	−0.680121	+	0.392668i	0.119779	+	0.992801i	$0.461781\pi$
$278$	−11.3161	−	6.53338i	−0.678697	−	0.391846i
$279$	0.740508	−	4.19963i	0.0443331	−	0.251425i
$280$		0			0
$281$	7.77732	+	6.52595i	0.463956	+	0.389305i	0.844584	−	0.535423i	$-0.179848\pi$
$281$	7.77732	+	6.52595i	0.463956	+	0.389305i	−0.380628	+	0.924728i	$0.624292\pi$
$282$	22.3768	−	3.94563i	1.33252	−	0.234959i
$283$	3.51037	−	9.64467i	0.208670	−	0.573316i	−0.790567	−	0.612376i	$-0.790214\pi$
$283$	3.51037	−	9.64467i	0.208670	−	0.573316i	0.999237	+	0.0390595i	$0.0124362\pi$
$284$	−13.3473			−0.792018
$285$		0			0
$286$	−4.18906			−0.247704
$287$	−4.41006	+	12.1165i	−0.260318	+	0.715217i
$288$	2.20251	−	0.388363i	0.129784	−	0.0228845i
$289$	0.547493	+	0.459401i	0.0322054	+	0.0270236i
$290$		0			0
$291$	3.05568	−	17.3296i	0.179127	−	1.01588i
$292$	−4.94384	−	2.85433i	−0.289316	−	0.167037i
$293$	6.18499	−	3.57090i	0.361331	−	0.208614i	−0.308334	−	0.951278i	$-0.599771\pi$
$293$	6.18499	−	3.57090i	0.361331	−	0.208614i	0.669664	+	0.742664i	$0.266438\pi$
$294$	1.43005	−	0.520494i	0.0834020	−	0.0303558i
$295$		0			0
$296$	−1.44674	−	2.50582i	−0.0840900	−	0.145648i
$297$	3.66362	+	2.11519i	0.212585	+	0.122736i
$298$	−2.04010	−	0.359724i	−0.118180	−	0.0208383i
$299$	11.8436	−	9.93793i	0.684931	−	0.574725i
$300$		0			0
$301$	−1.43092	−	8.11513i	−0.0824766	−	0.467748i
$302$	−1.21599	+	3.34091i	−0.0699725	+	0.192248i
$303$			24.0460i			1.38141i
$304$	4.28064	−	0.822290i	0.245511	−	0.0471615i
$305$		0			0
$306$	−8.48107	−	3.08686i	−0.484831	−	0.176464i
$307$	10.6573	−	1.87916i	0.608242	−	0.107250i	0.138960	−	0.990298i	$-0.455624\pi$
$307$	10.6573	−	1.87916i	0.608242	−	0.107250i	0.469282	+	0.883048i	$0.344513\pi$
$308$	4.30894	−	5.13519i	0.245524	−	0.292605i
$309$	−18.0745	+	15.1663i	−1.02822	+	0.862780i
$310$		0			0
$311$	−13.1789	+	22.8265i	−0.747307	+	1.29437i	0.201802	+	0.979426i	$0.435320\pi$
$311$	−13.1789	+	22.8265i	−0.747307	+	1.29437i	−0.949109	+	0.314947i	$0.898013\pi$
$312$	−3.42864	+	1.97952i	−0.194108	+	0.112068i
$313$	−10.3207	−	28.3558i	−0.583358	−	1.60276i	−0.782403	−	0.622772i	$-0.786006\pi$
$313$	−10.3207	−	28.3558i	−0.583358	−	1.60276i	0.199046	−	0.979990i	$-0.436216\pi$
$314$	8.65528	−	3.15027i	0.488446	−	0.177780i
$315$		0			0
$316$	−3.36233	+	5.82372i	−0.189146	+	0.327610i
$317$	−11.7732	−	2.07593i	−0.661248	−	0.116596i	−0.167054	−	0.985948i	$-0.553425\pi$
$317$	−11.7732	−	2.07593i	−0.661248	−	0.116596i	−0.494194	+	0.869352i	$0.664537\pi$
$318$	16.4463	+	19.5999i	0.922262	+	1.09911i
$319$	8.26015	+	6.93109i	0.462479	+	0.388066i
$320$		0			0
$321$	−15.1248	−	5.50499i	−0.844186	−	0.307259i
$322$			24.7409i			1.37875i
$323$	−16.6194	−	5.76348i	−0.924726	−	0.320689i
$324$	10.7076			0.594866
$325$		0			0
$326$	3.52661	+	20.0004i	0.195321	+	1.10772i
$327$	−9.18774	+	10.9495i	−0.508083	+	0.605510i
$328$	2.99367	+	3.56771i	0.165298	+	0.196994i
$329$	4.77368	−	27.0729i	0.263181	−	1.49258i
$330$		0			0
$331$	14.4811	+	25.0820i	0.795954	+	1.37863i	0.922232	+	0.386638i	$0.126364\pi$
$331$	14.4811	+	25.0820i	0.795954	+	1.37863i	−0.126277	+	0.991995i	$0.540303\pi$
$332$	−5.79840	−	15.9310i	−0.318229	−	0.874326i
$333$	2.21329	+	6.08097i	0.121288	+	0.333235i
$334$	−5.44777	−	9.43582i	−0.298089	−	0.516305i
$335$		0			0
$336$	1.10014	−	6.23920i	0.0600175	−	0.340376i
$337$	−2.86591	−	3.41545i	−0.156116	−	0.186052i	0.682317	−	0.731056i	$-0.260972\pi$
$337$	−2.86591	−	3.41545i	−0.156116	−	0.186052i	−0.838433	+	0.545005i	$0.816528\pi$
$338$	−6.43222	+	7.66562i	−0.349867	+	0.416955i
$339$	2.98231	+	16.9135i	0.161977	+	0.918617i
$340$		0			0
$341$	−4.61677			−0.250012
$342$	−9.74750	+	0.148666i	−0.527085	+	0.00803892i
$343$			17.5389i			0.947009i
$344$	−2.79687	−	1.01798i	−0.150797	−	0.0548857i
$345$		0			0
$346$	−12.8061	−	10.7456i	−0.688458	−	0.577684i
$347$	16.6023	+	19.7859i	0.891260	+	1.06216i	0.997696	+	0.0678428i	$0.0216116\pi$
$347$	16.6023	+	19.7859i	0.891260	+	1.06216i	−0.106436	+	0.994320i	$0.533944\pi$
$348$	10.0360	+	1.76961i	0.537985	+	0.0948613i
$349$	−10.9499	+	18.9659i	−0.586137	+	1.01522i	0.408595	+	0.912716i	$0.366019\pi$
$349$	−10.9499	+	18.9659i	−0.586137	+	1.01522i	−0.994733	+	0.102504i	$0.967315\pi$
$350$		0			0
$351$	−2.84047	+	1.03385i	−0.151613	+	0.0551827i
$352$	−0.828128	−	2.27526i	−0.0441394	−	0.121272i
$353$	11.0320	−	6.36930i	0.587172	−	0.339004i	−0.176807	−	0.984246i	$-0.556577\pi$
$353$	11.0320	−	6.36930i	0.587172	−	0.339004i	0.763978	+	0.645242i	$0.223243\pi$
$354$	2.30704	−	3.99590i	0.122618	−	0.212380i
$355$		0			0
$356$	4.25351	−	3.56912i	0.225436	−	0.189163i
$357$	−16.4340	+	19.5852i	−0.869778	+	1.03656i
$358$	−25.1529	+	4.43514i	−1.32937	+	0.234404i
$359$	23.3776	+	8.50877i	1.23382	+	0.449075i	0.874906	−	0.484293i	$-0.160923\pi$
$359$	23.3776	+	8.50877i	1.23382	+	0.449075i	0.358919	+	0.933369i	$0.383145\pi$
$360$		0			0
$361$	−18.9912	+	0.579428i	−0.999535	+	0.0304962i
$362$			2.09093i			0.109897i
$363$	4.02081	−	11.0471i	0.211038	−	0.579822i
$364$	0.831760	+	4.71714i	0.0435961	+	0.247246i
$365$		0			0
$366$	15.2596	−	12.8044i	0.797635	−	0.669295i
$367$	−10.9168	−	1.92492i	−0.569851	−	0.100480i	−0.118704	−	0.992930i	$-0.537874\pi$
$367$	−10.9168	−	1.92492i	−0.569851	−	0.100480i	−0.451147	+	0.892450i	$0.648985\pi$
$368$	7.73907	+	4.46815i	0.403427	+	0.232919i
$369$	−5.20803	−	9.02056i	−0.271119	−	0.469592i
$370$		0			0
$371$	29.0886	−	10.5874i	1.51021	−	0.549670i
$372$	−3.77871	+	2.18164i	−0.195917	+	0.113113i
$373$	−29.0060	−	16.7466i	−1.50188	−	0.867108i	−0.999998	−	0.00216955i	$-0.999309\pi$
$373$	−29.0060	−	16.7466i	−1.50188	−	0.867108i	−0.501878	−	0.864939i	$-0.667357\pi$
$374$	−1.69673	+	9.62266i	−0.0877360	+	0.497576i
$375$		0			0
$376$	−7.60641	−	6.38254i	−0.392271	−	0.329154i
$377$	−7.58770	+	1.33792i	−0.390786	+	0.0689062i
$378$	1.65441	−	4.54545i	0.0850937	−	0.233793i
$379$	−13.5486			−0.695946			−0.347973	−	0.937504i	$-0.613130\pi$
$379$	−13.5486			−0.695946			−0.347973	+	0.937504i	$0.613130\pi$
$380$		0			0
$381$	29.7651			1.52491
$382$	4.41448	−	12.1287i	0.225865	−	0.620558i
$383$	37.7833	−	6.66222i	1.93064	−	0.340423i	0.930943	−	0.365164i	$-0.118987\pi$
$383$	37.7833	−	6.66222i	1.93064	−	0.340423i	0.999694	+	0.0247406i	$0.00787597\pi$
$384$	−1.75297	−	1.47092i	−0.0894558	−	0.0750623i
$385$		0			0
$386$	−3.73231	+	21.1670i	−0.189969	+	1.07737i
$387$	5.76481	+	3.32831i	0.293042	+	0.169188i
$388$	−6.65961	+	3.84493i	−0.338090	+	0.195197i
$389$	12.5980	−	4.58528i	0.638742	−	0.232483i	−0.00228971	−	0.999997i	$-0.500729\pi$
$389$	12.5980	−	4.58528i	0.638742	−	0.232483i	0.641032	+	0.767514i	$0.278507\pi$
$390$		0			0
$391$	−18.0312	−	31.2310i	−0.911879	−	1.57942i
$392$	−0.575937	−	0.332517i	−0.0290892	−	0.0167947i
$393$	−10.5995	−	1.86898i	−0.534676	−	0.0942778i
$394$	8.69134	−	7.29290i	0.437863	−	0.367411i
$395$		0			0
$396$	0.940336	+	5.33291i	0.0472537	+	0.267989i
$397$	−10.3175	+	28.3472i	−0.517822	+	1.42270i	0.355094	+	0.934831i	$0.384449\pi$
$397$	−10.3175	+	28.3472i	−0.517822	+	1.42270i	−0.872915	+	0.487872i	$0.837773\pi$
$398$			13.5963i			0.681519i
$399$	−9.04825	+	26.0912i	−0.452979	+	1.30619i
$400$		0			0
$401$	−9.60460	−	3.49579i	−0.479631	−	0.174571i	0.0908794	−	0.995862i	$-0.471032\pi$
$401$	−9.60460	−	3.49579i	−0.479631	−	0.174571i	−0.570510	+	0.821291i	$0.693254\pi$
$402$	30.4079	−	5.36174i	1.51661	−	0.267419i
$403$	2.12046	−	2.52707i	0.105628	−	0.125882i
$404$	8.04966	−	6.75447i	0.400485	−	0.336047i
$405$		0			0
$406$	6.16475	−	10.6777i	0.305951	−	0.529923i
$407$	6.06731	−	3.50296i	0.300745	−	0.173635i
$408$	3.15842	+	8.67768i	0.156365	+	0.429609i
$409$	−23.6095	+	8.59314i	−1.16741	+	0.424904i	−0.851740	−	0.523964i	$-0.824452\pi$
$409$	−23.6095	+	8.59314i	−1.16741	+	0.424904i	−0.315673	+	0.948868i	$0.602230\pi$
$410$		0			0
$411$	25.2101	−	43.6652i	1.24352	−	2.15384i
$412$	10.1541	+	1.79045i	0.500258	+	0.0882091i
$413$	−3.58830	−	4.27637i	−0.176569	−	0.210426i
$414$	−15.3101	−	12.8467i	−0.752452	−	0.631382i
$415$		0			0
$416$	1.62576	+	0.591728i	0.0797094	+	0.0290119i
$417$		−	29.9012i		−	1.46427i
$418$	1.99100	+	10.3646i	0.0973828	+	0.506951i
$419$	4.75112			0.232107			0.116054	−	0.993243i	$-0.462976\pi$
$419$	4.75112			0.232107			0.116054	+	0.993243i	$0.462976\pi$
$420$		0			0
$421$	2.00373	+	11.3637i	0.0976559	+	0.553834i	0.993901	+	0.110275i	$0.0351732\pi$
$421$	2.00373	+	11.3637i	0.0976559	+	0.553834i	−0.896245	+	0.443559i	$0.853716\pi$
$422$	−2.86243	+	3.41131i	−0.139341	+	0.166060i
$423$	14.2745	+	17.0117i	0.694049	+	0.827136i
$424$	1.94156	−	11.0111i	0.0942904	−	0.534748i
$425$		0			0
$426$	−15.2716	−	26.4512i	−0.739911	−	1.28156i
$427$	−8.24288	−	22.6471i	−0.398901	−	1.09597i
$428$	2.40567	+	6.60953i	0.116283	+	0.319484i
$429$	−4.79299	−	8.30170i	−0.231408	−	0.400810i
$430$		0			0
$431$	1.50718	−	8.54765i	0.0725984	−	0.411726i	−0.926752	−	0.375675i	$-0.877411\pi$
$431$	1.50718	−	8.54765i	0.0725984	−	0.411726i	0.999350	−	0.0360511i	$-0.0114779\pi$
$432$	−1.12306	−	1.33841i	−0.0540331	−	0.0643942i
$433$	0.838704	−	0.999529i	0.0403056	−	0.0480343i	−0.745515	−	0.666489i	$-0.767796\pi$
$433$	0.838704	−	0.999529i	0.0403056	−	0.0480343i	0.785821	+	0.618454i	$0.212241\pi$
$434$	0.916684	+	5.19878i	0.0440023	+	0.249549i
$435$		0			0
$436$	6.24627			0.299142
$437$	−30.2177	−	24.5802i	−1.44551	−	1.17583i
$438$		−	13.0633i		−	0.624190i
$439$	−21.7294	−	7.90886i	−1.03709	−	0.377469i	−0.233313	−	0.972402i	$-0.574957\pi$
$439$	−21.7294	−	7.90886i	−1.03709	−	0.377469i	−0.803776	+	0.594932i	$0.797179\pi$
$440$		0			0
$441$	1.13937	+	0.956046i	0.0542558	+	0.0455260i
$442$	−4.48783	−	5.34838i	−0.213464	−	0.254397i
$443$	−31.3712	−	5.53159i	−1.49049	−	0.262814i	−0.631730	−	0.775189i	$-0.717655\pi$
$443$	−31.3712	−	5.53159i	−1.49049	−	0.262814i	−0.858762	+	0.512375i	$0.828766\pi$
$444$	3.31063	−	5.73417i	0.157115	−	0.272132i
$445$		0			0
$446$	18.6363	−	6.78306i	0.882454	−	0.321187i
$447$	−1.62133	−	4.45456i	−0.0766862	−	0.210694i
$448$	−2.39766	+	1.38429i	−0.113279	+	0.0654016i
$449$	−16.7627	+	29.0338i	−0.791080	+	1.37019i	0.134218	+	0.990952i	$0.457148\pi$
$449$	−16.7627	+	29.0338i	−0.791080	+	1.37019i	−0.925298	+	0.379240i	$0.876186\pi$
$450$		0			0
$451$	−8.63844	+	7.24852i	−0.406768	+	0.341319i
$452$	4.82426	−	5.74932i	0.226914	−	0.270425i
$453$	−8.01218	+	1.41276i	−0.376445	+	0.0663774i
$454$	−12.0605	−	4.38966i	−0.566027	−	0.206017i
$455$		0			0
$456$	6.52735	+	7.54235i	0.305671	+	0.353203i
$457$			2.81534i			0.131696i	0.997830	+	0.0658479i	$0.0209752\pi$
$457$			2.81534i			0.131696i	−0.997830	+	0.0658479i	$0.979025\pi$
$458$	3.92955	−	10.7963i	0.183616	−	0.504480i
$459$	1.22434	+	6.94358i	0.0571474	+	0.324099i
$460$		0			0
$461$	−6.64940	+	5.57951i	−0.309693	+	0.259864i	−0.784365	−	0.620299i	$-0.787011\pi$
$461$	−6.64940	+	5.57951i	−0.309693	+	0.259864i	0.474672	+	0.880163i	$0.342567\pi$
$462$	15.1069	+	2.66375i	0.702835	+	0.123929i
$463$	−16.4040	−	9.47085i	−0.762358	−	0.440148i	0.0677837	−	0.997700i	$-0.478407\pi$
$463$	−16.4040	−	9.47085i	−0.762358	−	0.440148i	−0.830142	+	0.557552i	$0.811741\pi$
$464$	−2.22668	−	3.85673i	−0.103371	−	0.179044i
$465$		0			0
$466$	2.56436	−	0.933350i	0.118792	−	0.0432366i
$467$	4.27919	−	2.47059i	0.198017	−	0.114325i	−0.397713	−	0.917510i	$-0.630196\pi$
$467$	4.27919	−	2.47059i	0.198017	−	0.114325i	0.595730	+	0.803184i	$0.296863\pi$
$468$	−3.35095	−	1.93467i	−0.154898	−	0.0894303i
$469$	6.48698	−	36.7895i	0.299541	−	1.69878i
$470$		0			0
$471$	16.1462	+	13.5482i	0.743976	+	0.624270i
$472$	−1.98571	+	0.350134i	−0.0913997	+	0.0161162i
$473$	2.46481	−	6.77202i	0.113332	−	0.311378i
$474$	−15.3883			−0.706807
$475$		0			0
$476$	11.1726			0.512096
$477$	−8.55262	+	23.4981i	−0.391598	+	1.07591i
$478$	24.6454	−	4.34565i	1.12725	−	0.198765i
$479$	19.4138	+	16.2901i	0.887038	+	0.744313i	0.967614	−	0.252435i	$-0.0812314\pi$
$479$	19.4138	+	16.2901i	0.887038	+	0.744313i	−0.0805757	+	0.996748i	$0.525676\pi$
$480$		0			0
$481$	−0.869282	+	4.92995i	−0.0396359	+	0.224786i
$482$	−21.8418	−	12.6104i	−0.994867	−	0.574387i
$483$	−49.0304	+	28.3077i	−2.23096	+	1.28805i
$484$	−4.82756	+	1.75709i	−0.219435	+	0.0798677i
$485$		0			0
$486$	9.63053	+	16.6806i	0.436850	+	0.756646i
$487$	−17.2918	−	9.98344i	−0.783567	−	0.452393i	0.0541258	−	0.998534i	$-0.482763\pi$
$487$	−17.2918	−	9.98344i	−0.783567	−	0.452393i	−0.837693	+	0.546141i	$0.816096\pi$
$488$	−8.57278	−	1.51161i	−0.388072	−	0.0684275i
$489$	−35.6009	+	29.8727i	−1.60993	+	1.35089i
$490$		0			0
$491$	−2.43814	−	13.8274i	−0.110032	−	0.624020i	−0.989091	−	0.147308i	$-0.952939\pi$
$491$	−2.43814	−	13.8274i	−0.110032	−	0.624020i	0.879059	−	0.476713i	$-0.158172\pi$
$492$	−3.64509	+	10.0148i	−0.164333	+	0.451502i
$493$			17.9716i			0.809399i
$494$	−6.58772	−	3.67063i	−0.296395	−	0.165149i
$495$		0			0
$496$	1.79175	+	0.652145i	0.0804521	+	0.0292822i
$497$	−36.3917	+	6.41684i	−1.63239	+	0.287835i
$498$	24.9370	−	29.7188i	1.11745	−	1.33173i
$499$	14.2758	−	11.9788i	0.639072	−	0.536245i	−0.264661	−	0.964341i	$-0.585260\pi$
$499$	14.2758	−	11.9788i	0.639072	−	0.536245i	0.903733	+	0.428097i	$0.140816\pi$
$500$		0			0
$501$	12.4663	−	21.5923i	0.556955	−	0.964674i
$502$	−2.89168	+	1.66951i	−0.129062	+	0.0745140i
$503$	−2.81271	−	7.72785i	−0.125412	−	0.344568i	0.861058	−	0.508507i	$-0.169802\pi$
$503$	−2.81271	−	7.72785i	−0.125412	−	0.344568i	−0.986470	+	0.163939i	$0.947580\pi$
$504$	5.81849	−	2.11776i	0.259176	−	0.0943323i
$505$		0			0
$506$	−10.8187	+	18.7385i	−0.480948	+	0.833027i
$507$	−22.5510	−	3.97634i	−1.00152	−	0.176596i
$508$	−8.36094	−	9.96418i	−0.370957	−	0.442089i
$509$	−20.2854	−	17.0215i	−0.899136	−	0.754465i	0.0708852	−	0.997484i	$-0.477418\pi$
$509$	−20.2854	−	17.0215i	−0.899136	−	0.754465i	−0.970021	+	0.243020i	$0.921862\pi$
$510$		0			0
$511$	−14.8517	−	5.40558i	−0.657001	−	0.239129i
$512$			1.00000i			0.0441942i
$513$	3.90800	+	6.53657i	0.172542	+	0.288597i
$514$	9.48495			0.418363
$515$		0			0
$516$	−1.18271	−	6.70747i	−0.0520658	−	0.295280i
$517$	15.4539	−	18.4173i	0.679663	−	0.809991i
$518$	−5.14926	−	6.13665i	−0.226245	−	0.269629i
$519$	6.64281	−	37.6732i	0.291587	−	1.65367i
$520$		0			0
$521$	−14.7837	−	25.6061i	−0.647686	−	1.12183i	−0.983674	−	0.179959i	$-0.942404\pi$
$521$	−14.7837	−	25.6061i	−0.647686	−	1.12183i	0.335988	−	0.941866i	$-0.390930\pi$
$522$	3.40649	+	9.35925i	0.149098	+	0.409643i
$523$	−0.839597	−	2.30677i	−0.0367130	−	0.100868i	0.919982	−	0.391961i	$-0.128203\pi$
$523$	−0.839597	−	2.30677i	−0.0367130	−	0.100868i	−0.956695	+	0.291093i	$0.905981\pi$
$524$	2.35172	+	4.07330i	0.102735	+	0.177943i
$525$		0			0
$526$	4.91064	−	27.8496i	0.214114	−	1.21430i
$527$	−4.94604	−	5.89447i	−0.215453	−	0.256767i
$528$	3.56150	−	4.24443i	0.154995	−	0.184715i
$529$	−9.87320	−	55.9937i	−0.429270	−	2.43451i
$530$		0			0
$531$	4.50953			0.195697
$532$	11.2759	−	4.29994i	0.488873	−	0.186426i
$533$		−	8.05761i		−	0.349014i
$534$	11.9399	+	4.34576i	0.516689	+	0.188059i
$535$		0			0
$536$	−10.3364	−	8.67326i	−0.446464	−	0.374628i
$537$	−37.5686	−	44.7725i	−1.62120	−	1.93207i
$538$	5.14589	+	0.907359i	0.221855	+	0.0391190i
$539$	0.805118	−	1.39451i	0.0346789	−	0.0600656i
$540$		0			0
$541$	−35.2607	+	12.8338i	−1.51597	+	0.551769i	−0.960139	−	0.279523i	$-0.909824\pi$
$541$	−35.2607	+	12.8338i	−1.51597	+	0.551769i	−0.555835	+	0.831293i	$0.687601\pi$
$542$	−0.123770	−	0.340055i	−0.00531637	−	0.0146066i
$543$	−4.14371	+	2.39237i	−0.177824	+	0.102667i
$544$	2.01775	−	3.49485i	0.0865104	−	0.149840i
$545$		0			0
$546$	−8.39657	+	7.04556i	−0.359340	+	0.301522i
$547$	−2.45730	+	2.92850i	−0.105067	+	0.125213i	−0.816015	−	0.578031i	$-0.803821\pi$
$547$	−2.45730	+	2.92850i	−0.105067	+	0.125213i	0.710949	+	0.703244i	$0.248266\pi$
$548$	−21.6988	+	3.82609i	−0.926927	+	0.163442i
$549$	18.2946	+	6.65870i	0.780795	+	0.284186i
$550$		0			0
$551$	6.91662	+	18.1377i	0.294658	+	0.772693i
$552$			20.4493i			0.870379i
$553$	−6.36764	+	17.4949i	−0.270780	+	0.743961i
$554$	2.26969	+	12.8720i	0.0964298	+	0.546880i
$555$		0			0
$556$	−10.0097	+	8.39915i	−0.424507	+	0.356203i
$557$	−2.33736	−	0.412140i	−0.0990373	−	0.0174629i	0.123910	−	0.992293i	$-0.460457\pi$
$557$	−2.33736	−	0.412140i	−0.0990373	−	0.0174629i	−0.222947	+	0.974831i	$0.571568\pi$
$558$	−3.69309	−	2.13221i	−0.156341	−	0.0902636i
$559$	2.57470	+	4.45952i	0.108898	+	0.188618i
$560$		0			0
$561$	−21.0111	+	7.64743i	−0.887091	+	0.322875i
$562$	8.79238	−	5.07629i	0.370884	−	0.214130i
$563$	15.9054	+	9.18301i	0.670335	+	0.387018i	0.796203	−	0.605029i	$-0.206838\pi$
$563$	15.9054	+	9.18301i	0.670335	+	0.387018i	−0.125869	+	0.992047i	$0.540172\pi$
$564$	3.94563	−	22.3768i	0.166141	−	0.942232i
$565$		0			0
$566$	−7.86241	−	6.59734i	−0.330482	−	0.277307i
$567$	29.1944	−	5.14776i	1.22605	−	0.216186i
$568$	−4.56505	+	12.5424i	−0.191545	+	0.526267i
$569$	−3.09691			−0.129829			−0.0649146	−	0.997891i	$-0.520678\pi$
$569$	−3.09691			−0.129829			−0.0649146	+	0.997891i	$0.520678\pi$
$570$		0			0
$571$	−21.1742			−0.886113			−0.443056	−	0.896494i	$-0.646106\pi$
$571$	−21.1742			−0.886113			−0.443056	+	0.896494i	$0.646106\pi$
$572$	−1.43274	+	3.93643i	−0.0599059	+	0.164590i
$573$	29.0870	−	5.12883i	1.21513	−	0.214260i
$574$	9.87750	+	8.28820i	0.412279	+	0.345943i
$575$		0			0
$576$	0.388363	−	2.20251i	0.0161818	−	0.0917714i
$577$	15.6935	+	9.06063i	0.653328	+	0.377199i	0.789730	−	0.613455i	$-0.210221\pi$
$577$	15.6935	+	9.06063i	0.653328	+	0.377199i	−0.136402	+	0.990654i	$0.543554\pi$
$578$	0.618949	−	0.357350i	0.0257449	−	0.0148638i
$579$	−46.2182	+	16.8220i	−1.92076	+	0.699100i
$580$		0			0
$581$	−23.4684	−	40.6485i	−0.973634	−	1.68638i
$582$	−15.2394	−	8.79849i	−0.631695	−	0.364709i
$583$	26.6611	+	4.70106i	1.10419	+	0.194698i
$584$	−4.37308	+	3.66945i	−0.180960	+	0.151843i
$585$		0			0
$586$	−1.24016	−	7.03331i	−0.0512306	−	0.290543i
$587$	2.62190	−	7.20361i	0.108217	−	0.297325i	−0.873750	−	0.486375i	$-0.838319\pi$
$587$	2.62190	−	7.20361i	0.108217	−	0.297325i	0.981967	+	0.189051i	$0.0605410\pi$
$588$		−	1.52182i		−	0.0627589i
$589$	−7.26034	−	4.04540i	−0.299157	−	0.166688i
$590$		0			0
$591$	24.3971	+	8.87983i	1.00356	+	0.365267i
$592$	−2.84952	+	0.502447i	−0.117114	+	0.0206504i
$593$	−0.814183	+	0.970306i	−0.0334345	+	0.0398457i	−0.782503	−	0.622647i	$-0.786057\pi$
$593$	−0.814183	+	0.970306i	−0.0334345	+	0.0398457i	0.749068	+	0.662493i	$0.230502\pi$
$594$	3.24066	−	2.71924i	0.132966	−	0.111572i
$595$		0			0
$596$	−1.03578	+	1.79403i	−0.0424274	+	0.0734864i
$597$	−26.9445	+	15.5564i	−1.10277	+	0.636682i
$598$	−5.28786	−	14.5283i	−0.216237	−	0.594106i
$599$	6.46096	−	2.35160i	0.263987	−	0.0960836i	−0.206636	−	0.978418i	$-0.566251\pi$
$599$	6.46096	−	2.35160i	0.263987	−	0.0960836i	0.470623	+	0.882334i	$0.344029\pi$
$600$		0			0
$601$	10.4282	−	18.0622i	0.425376	−	0.736772i	−0.571080	−	0.820895i	$-0.693475\pi$
$601$	10.4282	−	18.0622i	0.425376	−	0.736772i	0.996455	+	0.0841223i	$0.0268086\pi$
$602$	−8.11513	−	1.43092i	−0.330748	−	0.0583198i
$603$	19.3977	+	23.1172i	0.789934	+	0.941407i
$604$	2.72354	+	2.28532i	0.110819	+	0.0929883i
$605$		0			0
$606$	22.5959	+	8.22423i	0.917895	+	0.334087i
$607$			8.73323i			0.354471i	0.984168	+	0.177235i	$0.0567154\pi$
$607$			8.73323i			0.354471i	−0.984168	+	0.177235i	$0.943285\pi$
$608$	0.691364	−	4.30372i	0.0280385	−	0.174539i
$609$	28.2140			1.14329
$610$		0			0
$611$	2.98309	+	16.9180i	0.120683	+	0.684427i
$612$	−5.80140	+	6.91383i	−0.234508	+	0.279475i
$613$	13.9291	+	16.6001i	0.562591	+	0.670470i	0.970093	−	0.242734i	$-0.0780443\pi$
$613$	13.9291	+	16.6001i	0.562591	+	0.670470i	−0.407501	+	0.913205i	$0.633600\pi$
$614$	1.87916	−	10.6573i	0.0758369	−	0.430092i
$615$		0			0
$616$	−3.35176	−	5.80542i	−0.135046	−	0.233907i
$617$	4.07342	+	11.1916i	0.163990	+	0.450559i	0.994284	−	0.106767i	$-0.0340498\pi$
$617$	4.07342	+	11.1916i	0.163990	+	0.450559i	−0.830294	+	0.557325i	$0.811828\pi$
$618$	8.06981	+	22.1716i	0.324615	+	0.891874i
$619$	4.19167	+	7.26019i	0.168478	+	0.291812i	0.937885	−	0.346947i	$-0.112782\pi$
$619$	4.19167	+	7.26019i	0.168478	+	0.291812i	−0.769407	+	0.638759i	$0.779448\pi$
$620$		0			0
$621$	−2.71121	+	15.3760i	−0.108797	+	0.617018i
$622$	16.9425	+	20.1912i	0.679331	+	0.809595i
$623$	9.88139	−	11.7762i	0.395890	−	0.471803i
$624$	0.687481	+	3.89890i	0.0275213	+	0.156081i
$625$		0			0
$626$	−30.1756			−1.20606
$627$	−18.2622	+	15.8046i	−0.729321	+	0.631174i
$628$		−	9.21076i		−	0.367549i
$629$	10.9725	+	3.99365i	0.437500	+	0.159237i
$630$		0			0
$631$	34.4895	+	28.9401i	1.37301	+	1.15209i	0.971720	+	0.236135i	$0.0758807\pi$
$631$	34.4895	+	28.9401i	1.37301	+	1.15209i	0.401285	+	0.915953i	$0.368564\pi$
$632$	4.32252	+	5.15138i	0.171941	+	0.204911i
$633$	−10.0355	−	1.76953i	−0.398875	−	0.0703324i
$634$	−5.97740	+	10.3532i	−0.237393	+	0.411177i
$635$		0			0
$636$	24.0429	−	8.75089i	0.953362	−	0.346995i
$637$	0.393520	+	1.08119i	0.0155918	+	0.0428382i
$638$	9.33823	−	5.39143i	0.369704	−	0.213449i
$639$	14.9256	−	25.8519i	0.590447	−	1.02268i
$640$		0			0
$641$	−0.336944	+	0.282730i	−0.0133085	+	0.0111672i	−0.649418	−	0.760432i	$-0.724987\pi$
$641$	−0.336944	+	0.282730i	−0.0133085	+	0.0111672i	0.636109	+	0.771599i	$0.280543\pi$
$642$	−10.3460	+	12.3299i	−0.408324	+	0.486622i
$643$	5.39224	−	0.950798i	0.212649	−	0.0374958i	−0.0663085	−	0.997799i	$-0.521122\pi$
$643$	5.39224	−	0.950798i	0.212649	−	0.0374958i	0.278958	+	0.960303i	$0.410011\pi$
$644$	23.2488	+	8.46188i	0.916132	+	0.333445i
$645$		0			0
$646$	−11.1001	+	13.6459i	−0.436726	+	0.536889i
$647$			20.1149i			0.790797i	0.918510	+	0.395398i	$0.129393\pi$
$647$			20.1149i			0.790797i	−0.918510	+	0.395398i	$0.870607\pi$
$648$	3.66221	−	10.0618i	0.143865	−	0.395266i
$649$	−0.847774	−	4.80797i	−0.0332780	−	0.188729i
$650$		0			0
$651$	−9.25388	+	7.76493i	−0.362688	+	0.304331i
$652$	20.0004	+	3.52661i	0.783275	+	0.138113i
$653$	22.5556	+	13.0225i	0.882671	+	0.509610i	0.871538	−	0.490328i	$-0.163123\pi$
$653$	22.5556	+	13.0225i	0.882671	+	0.509610i	0.0111325	+	0.999938i	$0.496456\pi$
$654$	7.14679	+	12.3786i	0.279462	+	0.484042i
$655$		0			0
$656$	4.37645	−	1.59290i	0.170872	−	0.0621922i
$657$	11.0569	−	6.38368i	0.431369	−	0.249051i
$658$	−23.8075	−	13.7453i	−0.928112	−	0.535846i
$659$	0.984194	−	5.58164i	0.0383387	−	0.217430i	−0.959619	−	0.281302i	$-0.909234\pi$
$659$	0.984194	−	5.58164i	0.0383387	−	0.217430i	0.997958	+	0.0638720i	$0.0203449\pi$
$660$		0			0
$661$	−10.2769	−	8.62333i	−0.399724	−	0.335409i	0.420663	−	0.907217i	$-0.361798\pi$
$661$	−10.2769	−	8.62333i	−0.399724	−	0.335409i	−0.820387	+	0.571809i	$0.806242\pi$
$662$	28.5222	−	5.02924i	1.10855	−	0.195467i
$663$	5.46437	−	15.0132i	0.212219	−	0.583066i
$664$	−16.9534			−0.657919
$665$		0			0
$666$	6.47124			0.250755
$667$	−13.6112	+	37.3966i	−0.527029	+	1.44800i
$668$	−10.7300	+	1.89199i	−0.415157	+	0.0732033i
$669$	34.7654	+	29.1717i	1.34411	+	1.12784i
$670$		0			0
$671$	3.66004	−	20.7571i	0.141294	−	0.801320i
$672$	−5.48666	−	3.16772i	−0.211652	−	0.122198i
$673$	−26.5220	+	15.3125i	−1.02235	+	0.590252i	−0.914783	−	0.403946i	$-0.867638\pi$
$673$	−26.5220	+	15.3125i	−1.02235	+	0.590252i	−0.107564	+	0.994198i	$0.534305\pi$
$674$	−4.18967	+	1.52492i	−0.161380	+	0.0587376i
$675$		0			0
$676$	5.00338	+	8.66611i	0.192438	+	0.333312i
$677$	11.5683	+	6.67895i	0.444605	+	0.256693i	0.705549	−	0.708661i	$-0.250700\pi$
$677$	11.5683	+	6.67895i	0.444605	+	0.256693i	−0.260944	+	0.965354i	$0.584034\pi$
$678$	16.9135	+	2.98231i	0.649561	+	0.114535i
$679$	−16.3091	+	13.6849i	−0.625885	+	0.525179i
$680$		0			0
$681$	−5.10000	−	28.9235i	−0.195432	−	1.10835i
$682$	−1.57903	+	4.33834i	−0.0604641	+	0.166124i
$683$		−	9.75308i		−	0.373191i	−0.982437	−	0.186596i	$-0.940255\pi$
$683$		−	9.75308i		−	0.373191i	0.982437	−	0.186596i	$-0.0597454\pi$
$684$	−3.19414	+	9.21050i	−0.122131	+	0.352172i
$685$		0			0
$686$	16.4811	+	5.99864i	0.629253	+	0.229029i
$687$	25.8918	−	4.56543i	0.987835	−	0.174182i
$688$	−1.91317	+	2.28003i	−0.0729391	+	0.0869254i
$689$	−14.8185	+	12.4342i	−0.564541	+	0.473706i
$690$		0			0
$691$	−1.80854	+	3.13248i	−0.0688001	+	0.119165i	−0.898373	−	0.439233i	$-0.855250\pi$
$691$	−1.80854	+	3.13248i	−0.0688001	+	0.119165i	0.829573	+	0.558398i	$0.188584\pi$
$692$	−14.4774	+	8.35856i	−0.550350	+	0.317745i
$693$	5.12769	+	14.0882i	0.194785	+	0.535167i
$694$	24.2710	−	8.83392i	0.921314	−	0.335331i
$695$		0			0
$696$	5.09540	−	8.82549i	0.193141	−	0.334529i
$697$	−18.5091	−	3.26365i	−0.701082	−	0.123620i
$698$	14.0770	+	16.7763i	0.532822	+	0.634992i
$699$	4.78373	+	4.01403i	0.180937	+	0.151825i
$700$		0			0
$701$	−16.7716	−	6.10435i	−0.633453	−	0.230558i	0.00528040	−	0.999986i	$-0.498319\pi$
$701$	−16.7716	−	6.10435i	−0.633453	−	0.230558i	−0.638734	+	0.769428i	$0.720541\pi$
$702$			3.02277i			0.114087i
$703$	12.6109	−	0.192337i	0.475629	−	0.00725414i
$704$	−2.42128			−0.0912556
$705$		0			0
$706$	−2.21203	−	12.5451i	−0.0832510	−	0.472140i
$707$	18.7003	−	22.2861i	0.703296	−	0.838156i
$708$	−2.96587	−	3.53458i	−0.111464	−	0.132838i
$709$	6.05271	−	34.3266i	0.227314	−	1.28916i	−0.630897	−	0.775867i	$-0.717313\pi$
$709$	6.05271	−	34.3266i	0.227314	−	1.28916i	0.858211	−	0.513297i	$-0.171576\pi$
$710$		0			0
$711$	−7.51981	−	13.0247i	−0.282015	−	0.488464i
$712$	−1.89909	−	5.21770i	−0.0711714	−	0.195542i
$713$	−5.82777	−	16.0117i	−0.218252	−	0.599641i
$714$	12.7834	+	22.1414i	0.478405	+	0.828622i
$715$		0			0
$716$	−4.43514	+	25.1529i	−0.165749	+	0.940009i
$717$	36.8105	+	43.8691i	1.37472	+	1.63832i
$718$	15.9912	−	19.0576i	0.596788	−	0.711224i
$719$	3.64425	+	20.6676i	0.135908	+	0.770771i	0.974223	+	0.225586i	$0.0724296\pi$
$719$	3.64425	+	20.6676i	0.135908	+	0.770771i	−0.838316	+	0.545185i	$0.816459\pi$
$720$		0			0
$721$	28.5462			1.06312
$722$	−5.95088	+	18.0440i	−0.221469	+	0.671529i
$723$		−	57.7136i		−	2.14639i
$724$	1.96483	+	0.715139i	0.0730222	+	0.0265779i
$725$		0			0
$726$	−9.00568	−	7.55666i	−0.334232	−	0.280454i
$727$	−5.39689	−	6.43176i	−0.200159	−	0.238541i	0.656623	−	0.754219i	$-0.271984\pi$
$727$	−5.39689	−	6.43176i	−0.200159	−	0.238541i	−0.856782	+	0.515678i	$0.827540\pi$
$728$	4.71714	+	0.831760i	0.174829	+	0.0308271i
$729$	−5.97654	+	10.3517i	−0.221353	+	0.383395i
$730$		0			0
$731$	11.2868	−	4.10806i	0.417457	−	0.151942i
$732$	−6.81306	−	18.7187i	−0.251818	−	0.691864i
$733$	−7.51610	+	4.33942i	−0.277614	+	0.160280i	−0.632343	−	0.774689i	$-0.717906\pi$
$733$	−7.51610	+	4.33942i	−0.277614	+	0.160280i	0.354729	+	0.934969i	$0.384573\pi$
$734$	−5.54259	+	9.60005i	−0.204581	+	0.354344i
$735$		0			0
$736$	6.84561	−	5.74414i	0.252332	−	0.211732i
$737$	21.0004	−	25.0273i	0.773561	−	0.921894i
$738$	−10.2578	+	1.80873i	−0.377595	+	0.0665802i
$739$	9.63552	+	3.50704i	0.354448	+	0.129009i	0.513107	−	0.858325i	$-0.328495\pi$
$739$	9.63552	+	3.50704i	0.354448	+	0.129009i	−0.158658	+	0.987334i	$0.550717\pi$
$740$		0			0
$741$	−0.263169	−	17.2551i	−0.00966774	−	0.633881i
$742$		−	30.9555i		−	1.13641i
$743$	−11.7681	+	32.3326i	−0.431730	+	1.18617i	0.513020	+	0.858377i	$0.328527\pi$
$743$	−11.7681	+	32.3326i	−0.431730	+	1.18617i	−0.944750	+	0.327792i	$0.893695\pi$
$744$	0.757675	+	4.29699i	0.0277777	+	0.157535i
$745$		0			0
$746$	−25.6573	+	21.5291i	−0.939382	+	0.788235i
$747$	37.3401	+	6.58407i	1.36620	+	0.240898i
$748$	8.46202	+	4.88555i	0.309402	+	0.178633i
$749$	9.73670	+	16.8645i	0.355771	+	0.616214i
$750$		0			0
$751$	−3.94631	+	1.43634i	−0.144003	+	0.0524127i	−0.413016	−	0.910724i	$-0.635525\pi$
$751$	−3.94631	+	1.43634i	−0.144003	+	0.0524127i	0.269013	+	0.963136i	$0.413302\pi$
$752$	−8.59917	+	4.96473i	−0.313579	+	0.181045i
$753$	−6.61715	−	3.82041i	−0.241142	−	0.139224i
$754$	−1.33792	+	7.58770i	−0.0487240	+	0.276328i
$755$		0			0
$756$	−3.70549	−	3.10927i	−0.134767	−	0.113083i
$757$	14.1076	−	2.48755i	0.512749	−	0.0904115i	0.0887138	−	0.996057i	$-0.471724\pi$
$757$	14.1076	−	2.48755i	0.512749	−	0.0904115i	0.424035	+	0.905646i	$0.360613\pi$
$758$	−4.63390	+	12.7315i	−0.168311	+	0.462431i
$759$	−49.5135			−1.79723
$760$		0			0
$761$	15.6963			0.568992			0.284496	−	0.958677i	$-0.408174\pi$
$761$	15.6963			0.568992			0.284496	+	0.958677i	$0.408174\pi$
$762$	10.1803	−	27.9701i	0.368792	−	1.01325i
$763$	17.0306	−	3.00295i	0.616548	−	0.108714i
$764$	−9.88740	−	8.29651i	−0.357713	−	0.300157i
$765$		0			0
$766$	6.66222	−	37.7833i	0.240716	−	1.36517i
$767$	3.02110	+	1.74423i	0.109086	+	0.0629807i
$768$	−1.98176	+	1.14417i	−0.0715106	+	0.0412866i
$769$	−17.9278	+	6.52518i	−0.646492	+	0.235304i	−0.644394	−	0.764694i	$-0.722890\pi$
$769$	−17.9278	+	6.52518i	−0.646492	+	0.235304i	−0.00209836	+	0.999998i	$0.500668\pi$
$770$		0			0
$771$	10.8524	+	18.7969i	0.390839	+	0.676953i
$772$	18.6139	+	10.7467i	0.669929	+	0.386784i
$773$	−45.3434	−	7.99526i	−1.63089	−	0.287570i	−0.718081	−	0.695960i	$-0.754979\pi$
$773$	−45.3434	−	7.99526i	−1.63089	−	0.287570i	−0.912807	+	0.408390i	$0.866090\pi$
$774$	5.09927	−	4.27880i	0.183289	−	0.153798i
$775$		0			0
$776$	1.33533	+	7.57303i	0.0479355	+	0.271856i
$777$	6.26973	−	17.2259i	0.224925	−	0.617977i
$778$		−	13.4065i		−	0.480645i
$779$	−19.9363	+	3.82966i	−0.714291	+	0.137212i
$780$		0			0
$781$	−30.3687	−	11.0533i	−1.08668	−	0.395518i
$782$	−35.5146	+	6.26219i	−1.27000	+	0.223935i
$783$	5.00138	−	5.96041i	0.178735	−	0.213008i
$784$	−0.509446	+	0.427476i	−0.0181945	+	0.0152670i
$785$		0			0
$786$	−5.38153	+	9.32108i	−0.191953	+	0.332472i
$787$	45.8391	−	26.4652i	1.63399	−	0.943383i	0.651141	−	0.758956i	$-0.274290\pi$
$787$	45.8391	−	26.4652i	1.63399	−	0.943383i	0.982846	−	0.184427i	$-0.0590429\pi$
$788$	−3.88047	−	10.6615i	−0.138236	−	0.379800i
$789$	60.8098	−	22.1330i	2.16489	−	0.787954i
$790$		0			0
$791$	10.3894	−	17.9949i	0.369404	−	0.639827i
$792$	5.33291	+	0.940336i	0.189497	+	0.0334134i
$793$	9.68074	+	11.5371i	0.343773	+	0.409693i
$794$	23.1088	+	19.3906i	0.820101	+	0.688146i
$795$		0			0
$796$	12.7763	+	4.65019i	0.452844	+	0.164822i
$797$			40.6890i			1.44128i	0.693311	+	0.720639i	$0.256151\pi$
$797$			40.6890i			1.44128i	−0.693311	+	0.720639i	$0.743849\pi$
$798$	21.4230	+	17.4263i	0.758366	+	0.616883i
$799$	40.0704			1.41759
$800$		0			0
$801$	2.15641	+	12.2296i	0.0761929	+	0.432112i
$802$	−6.56993	+	7.82974i	−0.231992	+	0.276478i
$803$	−8.88479	−	10.5885i	−0.313537	−	0.373659i
$804$	5.36174	−	30.4079i	0.189094	−	1.07240i
$805$		0			0
$806$	−1.64943	−	2.85689i	−0.0580986	−	0.100630i
$807$	4.08960	+	11.2361i	0.143961	+	0.395529i
$808$	−3.59398	−	9.87437i	−0.126436	−	0.347379i
$809$	−2.30197	−	3.98714i	−0.0809331	−	0.140180i	0.822718	−	0.568450i	$-0.192457\pi$
$809$	−2.30197	−	3.98714i	−0.0809331	−	0.140180i	−0.903651	+	0.428270i	$0.859123\pi$
$810$		0			0
$811$	−5.75399	+	32.6325i	−0.202050	+	1.14588i	0.699965	+	0.714177i	$0.253199\pi$
$811$	−5.75399	+	32.6325i	−0.202050	+	1.14588i	−0.902015	+	0.431705i	$0.857912\pi$
$812$	−7.92524	−	9.44494i	−0.278122	−	0.331452i
$813$	0.532293	−	0.634362i	0.0186683	−	0.0222481i
$814$	−1.21657	−	6.89949i	−0.0426406	−	0.241827i
$815$		0			0
$816$	9.23460			0.323276
$817$	9.81010	−	8.48992i	0.343212	−	0.297025i
$818$			25.1247i			0.878464i
$819$	−10.0665	−	3.66392i	−0.351754	−	0.128028i
$820$		0			0
$821$	16.3258	+	13.6990i	0.569774	+	0.478098i	0.881571	−	0.472051i	$-0.156486\pi$
$821$	16.3258	+	13.6990i	0.569774	+	0.478098i	−0.311797	+	0.950149i	$0.600931\pi$
$822$	−32.4095	−	38.6241i	−1.13041	−	1.34717i
$823$	−47.1791	−	8.31895i	−1.64456	−	0.289980i	−0.726721	−	0.686933i	$-0.758957\pi$
$823$	−47.1791	−	8.31895i	−1.64456	−	0.289980i	−0.917839	+	0.396952i	$0.870068\pi$
$824$	5.15539	−	8.92940i	0.179597	−	0.311070i
$825$		0			0
$826$	−5.24574	+	1.90929i	−0.182523	+	0.0664329i
$827$	4.93122	+	13.5484i	0.171475	+	0.471125i	0.995426	−	0.0955370i	$-0.0304568\pi$
$827$	4.93122	+	13.5484i	0.171475	+	0.471125i	−0.823950	+	0.566662i	$0.808235\pi$
$828$	−17.3084	+	9.99298i	−0.601507	+	0.347280i
$829$	−3.14956	+	5.45520i	−0.109389	+	0.189467i	−0.915523	−	0.402266i	$-0.868223\pi$
$829$	−3.14956	+	5.45520i	−0.109389	+	0.189467i	0.806134	+	0.591733i	$0.201556\pi$
$830$		0			0
$831$	−22.9124	+	19.2258i	−0.794821	+	0.666934i
$832$	1.11209	−	1.32533i	0.0385546	−	0.0459476i
$833$	2.64298	−	0.466028i	0.0915737	−	0.0161469i
$834$	−28.0979	−	10.2268i	−0.972951	−	0.354125i
$835$		0			0
$836$	10.4205	+	1.67399i	0.360402	+	0.0578961i
$837$			3.33140i			0.115150i
$838$	1.62498	−	4.46459i	0.0561339	−	0.154227i
$839$	2.58965	+	14.6867i	0.0894048	+	0.507040i	0.996319	+	0.0857242i	$0.0273204\pi$
$839$	2.58965	+	14.6867i	0.0894048	+	0.507040i	−0.906914	+	0.421316i	$0.861568\pi$
$840$		0			0
$841$	−7.02276	+	5.89279i	−0.242164	+	0.203200i
$842$	11.3637	+	2.00373i	0.391620	+	0.0690532i
$843$	20.1199	+	11.6163i	0.692968	+	0.400085i
$844$	2.22657	+	3.85654i	0.0766418	+	0.132747i
$845$		0			0
$846$	20.8679	−	7.59529i	0.717453	−	0.261132i
$847$	−12.3177	+	7.11163i	−0.423241	+	0.244359i
$848$	−9.68302	−	5.59050i	−0.332516	−	0.191978i
$849$	4.07842	−	23.1299i	0.139971	−	0.793815i
$850$		0			0
$851$	19.8076	+	16.6206i	0.678996	+	0.569745i
$852$	−30.0792	+	5.30377i	−1.03050	+	0.181704i
$853$	19.6098	−	53.8776i	0.671428	−	1.84473i	0.156100	−	0.987741i	$-0.450108\pi$
$853$	19.6098	−	53.8776i	0.671428	−	1.84473i	0.515328	−	0.856993i	$-0.327670\pi$
$854$	−24.1006			−0.824705
$855$		0			0
$856$	7.03372			0.240407
$857$	7.80367	−	21.4404i	0.266568	−	0.732390i	−0.732120	−	0.681176i	$-0.761469\pi$
$857$	7.80367	−	21.4404i	0.266568	−	0.732390i	0.998688	−	0.0512138i	$-0.0163090\pi$
$858$	−9.44034	+	1.66459i	−0.322288	+	0.0568281i
$859$	18.2941	+	15.3506i	0.624188	+	0.523756i	0.899117	−	0.437709i	$-0.144210\pi$
$859$	18.2941	+	15.3506i	0.624188	+	0.523756i	−0.274929	+	0.961465i	$0.588654\pi$
$860$		0			0
$861$	−5.12370	+	29.0579i	−0.174615	+	0.990291i
$862$	−7.51668	−	4.33976i	−0.256019	−	0.147813i
$863$	−1.71748	+	0.991588i	−0.0584637	+	0.0337540i	−0.528947	−	0.848655i	$-0.677413\pi$
$863$	−1.71748	+	0.991588i	−0.0584637	+	0.0337540i	0.470483	+	0.882409i	$0.344080\pi$
$864$	−1.64180	+	0.597566i	−0.0558552	+	0.0203296i
$865$		0			0
$866$	−0.652396	−	1.12998i	−0.0221693	−	0.0383984i
$867$	1.41636	+	0.817739i	0.0481023	+	0.0277719i
$868$	5.19878	+	0.916684i	0.176458	+	0.0311143i
$869$	−12.4730	+	10.4661i	−0.423116	+	0.355036i
$870$		0			0
$871$	4.05374	+	22.9899i	0.137356	+	0.778983i
$872$	2.13635	−	5.86958i	0.0723460	−	0.198769i
$873$		−	17.1983i		−	0.582074i
$874$	−33.4329	+	19.9884i	−1.13088	+	0.676117i
$875$		0			0
$876$	−12.2755	−	4.46792i	−0.414751	−	0.150957i
$877$	8.80479	−	1.55252i	0.297317	−	0.0524250i	−0.0230000	−	0.999735i	$-0.507322\pi$
$877$	8.80479	−	1.55252i	0.297317	−	0.0524250i	0.320317	+	0.947311i	$0.396211\pi$
$878$	−14.8638	+	17.7140i	−0.501629	+	0.597818i
$879$	12.5194	−	10.5050i	0.422268	−	0.354325i
$880$		0			0
$881$	−17.8638	+	30.9409i	−0.601845	+	1.04243i	0.390696	+	0.920520i	$0.372234\pi$
$881$	−17.8638	+	30.9409i	−0.601845	+	1.04243i	−0.992542	+	0.121907i	$0.961099\pi$
$882$	1.28808	−	0.743672i	0.0433718	−	0.0250407i
$883$	16.3514	+	44.9250i	0.550268	+	1.51185i	0.833346	+	0.552751i	$0.186422\pi$
$883$	16.3514	+	44.9250i	0.550268	+	1.51185i	−0.283079	+	0.959097i	$0.591356\pi$
$884$	−6.56076	+	2.38792i	−0.220662	+	0.0803145i
$885$		0			0
$886$	−15.9276	+	27.5874i	−0.535098	+	0.926816i
$887$	−14.4771	−	2.55270i	−0.486093	−	0.0857112i	−0.0747695	−	0.997201i	$-0.523822\pi$
$887$	−14.4771	−	2.55270i	−0.486093	−	0.0857112i	−0.411323	+	0.911490i	$0.634933\pi$
$888$	−4.25606	−	5.07217i	−0.142824	−	0.170211i
$889$	−27.5866	−	23.1479i	−0.925226	−	0.776357i
$890$		0			0
$891$	24.3626	+	8.86724i	0.816176	+	0.297064i
$892$		−	19.8323i		−	0.664035i
$893$	40.4409	−	15.4217i	1.35330	−	0.516066i
$894$	−4.74045			−0.158544
$895$		0			0
$896$	0.480759	+	2.72652i	0.0160610	+	0.0910866i
$897$	22.7413	−	27.1021i	0.759311	−	0.904912i
$898$	21.5497	+	25.6819i	0.719123	+	0.857017i
$899$	−1.47452	+	8.36242i	−0.0491780	+	0.278902i
$900$		0			0
$901$	22.5605	+	39.0759i	0.751598	+	1.30181i
$902$	3.85685	+	10.5966i	0.128419	+	0.352829i
$903$	−6.44935	−	17.7194i	−0.214621	−	0.589666i
$904$	−3.75261	−	6.49970i	−0.124810	−	0.216177i
$905$		0			0
$906$	−1.41276	+	8.01218i	−0.0469359	+	0.266187i
$907$	−31.1582	−	37.1329i	−1.03459	−	1.23298i	−0.972011	−	0.234936i	$-0.924512\pi$
$907$	−31.1582	−	37.1329i	−1.03459	−	1.23298i	−0.0625793	−	0.998040i	$-0.519933\pi$
$908$	−8.24987	+	9.83181i	−0.273782	+	0.326280i
$909$	4.08095	+	23.1442i	0.135356	+	0.767644i
$910$		0			0
$911$	−1.23529			−0.0409271			−0.0204635	−	0.999791i	$-0.506514\pi$
$911$	−1.23529			−0.0409271			−0.0204635	+	0.999791i	$0.506514\pi$
$912$	9.31997	−	3.55407i	0.308615	−	0.117687i
$913$		−	41.0490i		−	1.35852i
$914$	2.64555	+	0.962902i	0.0875070	+	0.0318500i
$915$		0			0
$916$	−8.80126	−	7.38514i	−0.290802	−	0.244012i
$917$	8.37028	+	9.97531i	0.276411	+	0.329414i
$918$	6.94358	+	1.22434i	0.229172	+	0.0404093i
$919$	−2.15131	+	3.72618i	−0.0709652	+	0.122915i	−0.899325	−	0.437282i	$-0.855941\pi$
$919$	−2.15131	+	3.72618i	−0.0709652	+	0.122915i	0.828359	+	0.560197i	$0.189275\pi$
$920$		0			0
$921$	23.2702	−	8.46966i	0.766780	−	0.279085i
$922$	2.96880	+	8.15670i	0.0977721	+	0.268627i
$923$	19.9984	−	11.5461i	0.658255	−	0.380044i
$924$	7.66996	−	13.2848i	0.252323	−	0.437036i
$925$		0			0
$926$	−14.5102	+	12.1755i	−0.476834	+	0.400111i
$927$	−14.8227	+	17.6650i	−0.486840	+	0.580193i
$928$	−4.38571	+	0.773318i	−0.143968	+	0.0253854i
$929$	32.8280	+	11.9484i	1.07705	+	0.392015i	0.818810	−	0.574065i	$-0.194634\pi$
$929$	32.8280	+	11.9484i	1.07705	+	0.392015i	0.258242	+	0.966080i	$0.416857\pi$
$930$		0			0
$931$	2.48805	−	1.48752i	0.0815427	−	0.0487516i
$932$		−	2.72893i		−	0.0893892i
$933$	−20.6291	+	56.6781i	−0.675368	+	1.85556i
$934$	−0.858028	−	4.86612i	−0.0280755	−	0.159224i
$935$		0			0
$936$	−2.96409	+	2.48717i	−0.0968844	+	0.0812956i
$937$	2.50293	+	0.441335i	0.0817673	+	0.0144178i	0.214382	−	0.976750i	$-0.431226\pi$
$937$	2.50293	+	0.441335i	0.0817673	+	0.0144178i	−0.132615	+	0.991168i	$0.542337\pi$
$938$	−32.3521	−	18.6785i	−1.05633	−	0.609875i
$939$	−34.5260	−	59.8007i	−1.12671	−	1.95152i
$940$		0			0
$941$	−19.8302	+	7.21759i	−0.646445	+	0.235287i	−0.644373	−	0.764711i	$-0.722882\pi$
$941$	−19.8302	+	7.21759i	−0.646445	+	0.235287i	−0.00207156	+	0.999998i	$0.500659\pi$
$942$	18.2535	−	10.5387i	0.594731	−	0.343368i
$943$	−36.0433	−	20.8096i	−1.17373	−	0.677654i
$944$	−0.350134	+	1.98571i	−0.0113959	+	0.0646293i
$945$		0			0
$946$	−5.52060	−	4.63234i	−0.179490	−	0.150610i
$947$	38.3965	−	6.77033i	1.24772	−	0.220006i	0.489497	−	0.872005i	$-0.337180\pi$
$947$	38.3965	−	6.77033i	1.24772	−	0.220006i	0.758220	+	0.651999i	$0.226069\pi$
$948$	−5.26310	+	14.4602i	−0.170938	+	0.469647i
$949$	9.87653			0.320606
$950$		0			0
$951$	−27.3566			−0.887099
$952$	3.82126	−	10.4988i	0.123848	−	0.340269i
$953$	21.5051	−	3.79192i	0.696618	−	0.122832i	0.185884	−	0.982572i	$-0.440485\pi$
$953$	21.5051	−	3.79192i	0.696618	−	0.122832i	0.510733	+	0.859739i	$0.329374\pi$
$954$	19.1558	+	16.0737i	0.620194	+	0.520404i
$955$		0			0
$956$	4.34565	−	24.6454i	0.140548	−	0.797090i
$957$	21.3690	+	12.3374i	0.690762	+	0.398812i
$958$	21.9476	−	12.6714i	0.709094	−	0.409396i
$959$	−57.3228	+	20.8638i	−1.85105	+	0.673727i
$960$		0			0
$961$	13.6822	+	23.6982i	0.441360	+	0.764458i
$962$	4.33532	+	2.50300i	0.139776	+	0.0806999i
$963$	−15.4919	−	2.73163i	−0.499218	−	0.0880256i
$964$	−19.3202	+	16.2116i	−0.622262	+	0.522140i
$965$		0			0
$966$	9.83117	+	55.7554i	0.316313	+	1.79390i
$967$	3.40380	−	9.35186i	0.109459	−	0.300736i	−0.872854	−	0.487981i	$-0.837734\pi$
$967$	3.40380	−	9.35186i	0.109459	−	0.300736i	0.982313	+	0.187245i	$0.0599559\pi$
$968$			5.13739i			0.165122i
$969$	−39.7431	−	6.38447i	−1.27673	−	0.205099i
$970$		0			0
$971$	17.9288	+	6.52554i	0.575362	+	0.209415i	0.613279	−	0.789866i	$-0.289850\pi$
$971$	17.9288	+	6.52554i	0.575362	+	0.209415i	−0.0379172	+	0.999281i	$0.512072\pi$
$972$	18.9684	−	3.34465i	0.608413	−	0.107280i
$973$	−23.2537	+	27.7127i	−0.745480	+	0.888429i
$974$	−15.2955	+	12.8345i	−0.490100	+	0.411243i
$975$		0			0
$976$	−4.35252	+	7.53878i	−0.139321	+	0.241310i
$977$	−9.54886	+	5.51304i	−0.305495	+	0.176378i	−0.644909	−	0.764260i	$-0.723105\pi$
$977$	−9.54886	+	5.51304i	−0.305495	+	0.176378i	0.339414	+	0.940637i	$0.389771\pi$
$978$	15.8949	+	43.6710i	0.508264	+	1.39644i
$979$	12.6335	−	4.59823i	0.403770	−	0.146960i
$980$		0			0
$981$	−6.98487	+	12.0981i	−0.223010	+	0.386264i
$982$	−13.8274	−	2.43814i	−0.441249	−	0.0778041i
$983$	3.23425	+	3.85443i	0.103157	+	0.122937i	0.815153	−	0.579246i	$-0.196653\pi$
$983$	3.23425	+	3.85443i	0.103157	+	0.122937i	−0.711996	+	0.702184i	$0.752209\pi$
$984$	8.16413	+	6.85052i	0.260263	+	0.218387i
$985$		0			0
$986$	16.8878	+	6.14664i	0.537816	+	0.195749i
$987$		−	62.9076i		−	2.00237i
$988$	−5.70239	+	4.93500i	−0.181417	+	0.157003i
$989$	26.5977			0.845759
$990$		0			0
$991$	−8.36382	−	47.4336i	−0.265686	−	1.50678i	−0.767076	−	0.641556i	$-0.778289\pi$
$991$	−8.36382	−	47.4336i	−0.265686	−	1.50678i	0.501390	−	0.865221i	$-0.332822\pi$
$992$	1.22563	−	1.46065i	0.0389139	−	0.0463757i
$993$	42.6010	+	50.7699i	1.35190	+	1.61113i
$994$	−6.41684	+	36.3917i	−0.203530	+	1.15428i
$995$		0			0
$996$	−19.3976	−	33.5975i	−0.614635	−	1.06458i
$997$	−10.4731	−	28.7745i	−0.331685	−	0.911298i	−0.987674	−	0.156527i	$-0.949970\pi$
$997$	−10.4731	−	28.7745i	−0.331685	−	0.911298i	0.655988	−	0.754771i	$-0.272252\pi$
$998$	−6.37379	−	17.5118i	−0.201759	−	0.554327i
$999$	−2.52769	−	4.37809i	−0.0799727	−	0.138517i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.u.f.99.4		24
5.2	odd	4		950.2.l.g.251.1		12
5.3	odd	4		190.2.k.c.61.2	✓	12
5.4	even	2	inner	950.2.u.f.99.1		24
19.5	even	9	inner	950.2.u.f.499.1		24
95.24	even	18	inner	950.2.u.f.499.4		24
95.28	odd	36		3610.2.a.bf.1.5		6
95.43	odd	36		190.2.k.c.81.2	yes	12
95.48	even	36		3610.2.a.bd.1.2		6
95.62	odd	36		950.2.l.g.651.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.k.c.61.2	✓	12	5.3	odd	4
190.2.k.c.81.2	yes	12	95.43	odd	36
950.2.l.g.251.1		12	5.2	odd	4
950.2.l.g.651.1		12	95.62	odd	36
950.2.u.f.99.1		24	5.4	even	2	inner
950.2.u.f.99.4		24	1.1	even	1	trivial
950.2.u.f.499.1		24	19.5	even	9	inner
950.2.u.f.499.4		24	95.24	even	18	inner
3610.2.a.bd.1.2		6	95.48	even	36
3610.2.a.bf.1.5		6	95.28	odd	36

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.u (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.342020 - 0.939693i) q^{2} +(2.25357 - 0.397366i) q^{3} +(-0.766044 - 0.642788i) q^{4} +(0.397366 - 2.25357i) q^{6} +(-2.39766 - 1.38429i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(2.10161 - 0.764925i) q^{9} +O(q^{10})\)	\(q+(0.342020 - 0.939693i) q^{2} +(2.25357 - 0.397366i) q^{3} +(-0.766044 - 0.642788i) q^{4} +(0.397366 - 2.25357i) q^{6} +(-2.39766 - 1.38429i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(2.10161 - 0.764925i) q^{9} +(-1.21064 - 2.09689i) q^{11} +(-1.98176 - 1.14417i) q^{12} +(1.70381 + 0.300428i) q^{13} +(-2.12086 + 1.77961i) q^{14} +(0.173648 + 0.984808i) q^{16} +(1.38022 - 3.79213i) q^{17} -2.23649i q^{18} +(-0.0664727 - 4.35839i) q^{19} +(-5.95337 - 2.16685i) q^{21} +(-2.38450 + 0.420451i) q^{22} +(5.74414 - 6.84561i) q^{23} +(-1.75297 + 1.47092i) q^{24} +(0.865049 - 1.49831i) q^{26} +(-1.51309 + 0.873583i) q^{27} +(0.946910 + 2.60161i) q^{28} +(-4.18479 + 1.52314i) q^{29} +(0.953372 - 1.65129i) q^{31} +(0.984808 + 0.173648i) q^{32} +(-3.56150 - 4.24443i) q^{33} +(-3.09138 - 2.59397i) q^{34} +(-2.10161 - 0.764925i) q^{36} +2.89348i q^{37} +(-4.11828 - 1.42819i) q^{38} +3.95905 q^{39} +(-0.808735 - 4.58656i) q^{41} +(-4.07235 + 4.85323i) q^{42} +(1.91317 + 2.28003i) q^{43} +(-0.420451 + 2.38450i) q^{44} +(-4.46815 - 7.73907i) q^{46} +(3.39608 + 9.33064i) q^{47} +(0.782658 + 2.15033i) q^{48} +(0.332517 + 0.575937i) q^{49} +(1.60357 - 9.09430i) q^{51} +(-1.11209 - 1.32533i) q^{52} +(-7.18700 + 8.56514i) q^{53} +(0.303392 + 1.72062i) q^{54} +2.76858 q^{56} +(-1.88168 - 9.79554i) q^{57} +4.45336i q^{58} +(1.89474 + 0.689630i) q^{59} +(6.66844 + 5.59549i) q^{61} +(-1.22563 - 1.46065i) q^{62} +(-6.09783 - 1.07521i) q^{63} +(0.500000 - 0.866025i) q^{64} +(-5.20657 + 1.89504i) q^{66} +(4.61495 + 12.6795i) q^{67} +(-3.49485 + 2.01775i) q^{68} +(10.2246 - 17.7096i) q^{69} +(10.2246 - 8.57949i) q^{71} +(-1.43759 + 1.71325i) q^{72} +(5.62193 - 0.991298i) q^{73} +(2.71898 + 0.989627i) q^{74} +(-2.75060 + 3.38145i) q^{76} +6.70352i q^{77} +(1.35407 - 3.72029i) q^{78} +(-1.16772 - 6.62249i) q^{79} +(-8.20248 + 6.88270i) q^{81} +(-4.58656 - 0.808735i) q^{82} +(14.6821 + 8.47670i) q^{83} +(3.16772 + 5.48666i) q^{84} +(2.79687 - 1.01798i) q^{86} +(-8.82549 + 5.09540i) q^{87} +(2.09689 + 1.21064i) q^{88} +(-0.964193 + 5.46821i) q^{89} +(-3.66929 - 3.07890i) q^{91} +(-8.80054 + 1.55177i) q^{92} +(1.49233 - 4.10014i) q^{93} +9.92946 q^{94} +2.28834 q^{96} +(2.63009 - 7.22610i) q^{97} +(0.654931 - 0.115482i) q^{98} +(-4.14827 - 3.48081i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{6} - 18 q^{9}+O(q^{10}) \) 24 * q + 6 * q^6 - 18 * q^9	\( 24 q + 6 q^{6} - 18 q^{9} - 12 q^{11} + 12 q^{14} - 12 q^{19} - 72 q^{21} - 6 q^{24} - 6 q^{26} - 72 q^{29} - 48 q^{31} + 12 q^{34} + 18 q^{36} + 24 q^{39} - 24 q^{41} + 18 q^{44} - 36 q^{46} - 54 q^{51} - 18 q^{54} + 24 q^{56} + 54 q^{59} + 108 q^{61} + 12 q^{64} - 78 q^{66} + 48 q^{69} + 48 q^{71} - 30 q^{74} + 18 q^{76} + 72 q^{79} - 18 q^{81} - 24 q^{84} + 48 q^{86} - 36 q^{89} + 24 q^{91} - 36 q^{94} - 36 q^{99}+O(q^{100}) \) 24 * q + 6 * q^6 - 18 * q^9 - 12 * q^11 + 12 * q^14 - 12 * q^19 - 72 * q^21 - 6 * q^24 - 6 * q^26 - 72 * q^29 - 48 * q^31 + 12 * q^34 + 18 * q^36 + 24 * q^39 - 24 * q^41 + 18 * q^44 - 36 * q^46 - 54 * q^51 - 18 * q^54 + 24 * q^56 + 54 * q^59 + 108 * q^61 + 12 * q^64 - 78 * q^66 + 48 * q^69 + 48 * q^71 - 30 * q^74 + 18 * q^76 + 72 * q^79 - 18 * q^81 - 24 * q^84 + 48 * q^86 - 36 * q^89 + 24 * q^91 - 36 * q^94 - 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more